{"id":53590,"date":"2020-06-11T14:30:26","date_gmt":"2020-06-11T13:30:26","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=53590"},"modified":"2026-10-17T12:54:04","modified_gmt":"2026-10-17T11:54:04","slug":"cours-en-ligne-racines-carrees","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/","title":{"rendered":"Cours sur les racines carr\u00e9es"},"content":{"rendered":"<div class=\"Latex_page\">\n<section class=\"has_ae_slider elementor-element elementor-section-full_width elementor-reverse-mobile elementor-section-stretched elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default elementor-section elementor-top-section\">\n<div class=\"elementor-container elementor-column-gap-no\">\n<div class=\"elementor-row\">\n<div class=\"elementor-column-wrap elementor-element-populated colone_elementor\">\n<p style=\"text-align: justify;\">\t\t<div data-elementor-type=\"page\" data-elementor-id=\"86176\" class=\"elementor elementor-86176\">\n\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-6f9fb2b3 elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"6f9fb2b3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5032621c sticky_badeau_colone strick_col ae-bg-gallery-type-default\" data-id=\"5032621c\" data-element_type=\"column\" data-e-type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-611bd75f elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"611bd75f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-55718945 strick_col ae-bg-gallery-type-default\" data-id=\"55718945\" data-element_type=\"column\" data-e-type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5940f45c elementor-widget elementor-widget-heading\" data-id=\"5940f45c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne Tage Mage <\/a><\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9bc725 elementor-widget elementor-widget-heading\" data-id=\"f9bc725\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Chapitres du sous-test 2 du Tage Mage<\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56c02cf0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"56c02cf0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Fractions<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-390da5ff elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"390da5ff\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pourcentages\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pourcentages<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da8d658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"da8d658\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-algebre\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Alg\u00e8bre<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-490ac2aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"490ac2aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">G\u00e9om\u00e9trie<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3fd40310 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3fd40310\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-vitesse\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Vitesse<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6edf1c7e elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6edf1c7e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Arithm\u00e9tique<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4f2c805 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4f2c805\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-puissances\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Puissances<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-447b658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"447b658\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-regle-de-trois\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Proportionnalit\u00e9<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53863aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"53863aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-denombrement\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9nombrement<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11741389 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"11741389\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Probabilit\u00e9s<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ace8ace elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6ace8ace\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-moyenne-arithmetique-moyenne-ponderee\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Moyenne<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-13f1db2f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"13f1db2f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Th\u00e9or\u00e8me de Pythagore<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-10d04684 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"10d04684\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-thales\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Th\u00e9or\u00e8me de Thal\u00e8s<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-691a3a8a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"691a3a8a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Racines Carr\u00e9es<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2a5f7bd6 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2a5f7bd6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/groupe-reussite.fr\/nous-contacter\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">CONTACTEZ-NOUS<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"elementor-column-wrap elementor-element-populated colone_latex\">\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<div class=\"elementor-text-editor elementor-clearfix\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: justify;\">\n<h1 class=\"Latex_page_title\">Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau<\/h1>\n<p dir=\"ltr\"><em>Par Seda Biber, mis \u00e0 jour le 17\/10\/2026<\/em><\/p>\n<p dir=\"ltr\">La <strong>racine carr\u00e9e<\/strong> d\u2019un nombre positif <em>a<\/em>, not\u00e9e <strong>\u221aa<\/strong>, est le nombre <strong>positif<\/strong> dont le carr\u00e9 est \u00e9gal \u00e0 <em>a<\/em>. Par exemple, \u221a9 = 3 car 3\u00b2 = 9, et \u221a100 = 10 car 10\u00b2 = 100. Quand le nombre n\u2019est pas un carr\u00e9 parfait, sa racine carr\u00e9e n\u2019est pas un nombre entier : \u221a3 \u2248 1,732. La racine carr\u00e9e d\u2019un nombre n\u00e9gatif n\u2019existe pas parmi les nombres r\u00e9els.<\/p>\n<\/div>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-racines-carrees\/\">Exercices et corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\" style=\"color: #000000; font-family: Lato, sans-serif; text-align: center;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne du Tage Mage<\/a><\/p>\n<h2 dir=\"ltr\">R\u00e9sum\u00e9 : l\u2019essentiel sur les racines carr\u00e9es<\/h2>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Notion<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>\u00c0 retenir<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Exemple<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">D\u00e9finition<\/td>\n<td style=\"border: 1px solid #0F2742;\">Pour a \u2265 0, \u221aa est le nombre positif dont le carr\u00e9 vaut a<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a49 = 7 car 7\u00b2 = 49<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Carr\u00e9 d\u2019une racine<\/td>\n<td style=\"border: 1px solid #0F2742;\">(\u221aa)\u00b2 = a, pour a \u2265 0<\/td>\n<td style=\"border: 1px solid #0F2742;\">(\u221a3)\u00b2 = 3<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Produit<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a(a \u00d7 b) = \u221aa \u00d7 \u221ab, pour a \u2265 0 et b \u2265 0<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a12 = \u221a4 \u00d7 \u221a3 = 2\u221a3<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Quotient<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a(a \/ b) = \u221aa \/ \u221ab, pour a \u2265 0 et b &gt; 0<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a(9\/25) = 3\/5<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Somme<\/td>\n<td style=\"border: 1px solid #0F2742;\"><strong>Aucune formule<\/strong> : \u221a(a + b) n\u2019est pas \u00e9gal \u00e0 \u221aa + \u221ab<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a(9 + 16) = 5, mais \u221a9 + \u221a16 = 7<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Valeurs \u00e0 conna\u00eetre<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a2 \u2248 1,414 ; \u221a3 \u2248 1,732 ; \u221a5 \u2248 2,236<\/td>\n<td style=\"border: 1px solid #0F2742;\">Ces racines ne sont pas des nombres d\u00e9cimaux<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 dir=\"ltr\">Qu\u2019est-ce qu\u2019une racine carr\u00e9e ?<\/h2>\n<p dir=\"ltr\">Chercher la racine carr\u00e9e de <em>a<\/em>, c\u2019est r\u00e9pondre \u00e0 la question : <strong>quel nombre positif, multipli\u00e9 par lui-m\u00eame, donne <em>a<\/em> ?<\/strong><\/p>\n<ul dir=\"ltr\">\n<li>\u221a25 = 5, car 5 \u00d7 5 = 25.<\/li>\n<li>\u221a0 = 0, car 0 \u00d7 0 = 0.<\/li>\n<li>\u221a7 n\u2019est pas un entier. C\u2019est le nombre positif qui, au carr\u00e9, vaut 7 : \u221a7 \u2248 2,646.<\/li>\n<\/ul>\n<p dir=\"ltr\">Le signe \u221a s\u2019appelle le <strong>radical<\/strong> et le nombre \u00e9crit dessous s\u2019appelle le <strong>radicande<\/strong>. La racine carr\u00e9e est l\u2019op\u00e9ration inverse du carr\u00e9 pour les nombres positifs. On peut aussi l\u2019\u00e9crire sous forme de <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-puissances\/\">puissance<\/a> : \u221aa = a^(1\/2).<\/p>\n<p dir=\"ltr\">Attention, (\u22125)\u00b2 = 25 aussi. Mais par d\u00e9finition, \u221a25 vaut 5 et non \u22125 : une racine carr\u00e9e est toujours positive. L\u2019\u00e9quation x\u00b2 = 25 a donc deux solutions, 5 et \u22125, c\u2019est-\u00e0-dire \u221a25 et \u2212\u221a25.<\/p>\n<p dir=\"ltr\">Au coll\u00e8ge (cycle 4), le programme demande de conna\u00eetre la d\u00e9finition, d\u2019encadrer la racine carr\u00e9e d\u2019un entier entre deux entiers cons\u00e9cutifs et de r\u00e9soudre des \u00e9quations du type x\u00b2 = a. En seconde, on d\u00e9montre la formule du produit et on calcule avec des racines carr\u00e9es. Ces calculs sont aussi utiles pour le sous-test 2 de notre <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">cours en ligne du Tage Mage<\/a>.<\/p>\n<p dir=\"ltr\">\t\t<div data-elementor-type=\"section\" data-elementor-id=\"84983\" class=\"elementor elementor-84983\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-51d9c4d elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"51d9c4d\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-610eeeb9 ae-bg-gallery-type-default\" data-id=\"610eeeb9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5bf69eb8 elementor-widget elementor-widget-heading\" data-id=\"5bf69eb8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">COURS DE MATHS<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49568da4 elementor-widget elementor-widget-heading\" data-id=\"49568da4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les meilleurs professeurs particuliers<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1eb9e0cb elementor-widget elementor-widget-heading\" data-id=\"1eb9e0cb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Pour progresser et r\u00e9ussir<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-15c3e28d elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"15c3e28d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-md\" href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours particuliers maths<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1a5c10e7 elementor-widget elementor-widget-text-editor\" data-id=\"1a5c10e7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: left\"><b>Avis Google France <\/b><span style=\"color: #e5a430\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6913d4fe ae-bg-gallery-type-default\" data-id=\"6913d4fe\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<h2 dir=\"ltr\">Tableau des racines carr\u00e9es de 0 \u00e0 441<\/h2>\n<p dir=\"ltr\">Les nombres de ce tableau sont des <strong>carr\u00e9s parfaits<\/strong> : leur racine carr\u00e9e est un nombre entier. Les conna\u00eetre par c\u0153ur vous fera gagner du temps dans tous les calculs.<\/p>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Nombre<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Racine carr\u00e9e<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Nombre<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Racine carr\u00e9e<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">0<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a0 = 0<\/td>\n<td style=\"border: 1px solid #0F2742;\">121<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a121 = 11<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">1<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a1 = 1<\/td>\n<td style=\"border: 1px solid #0F2742;\">144<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a144 = 12<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">4<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a4 = 2<\/td>\n<td style=\"border: 1px solid #0F2742;\">169<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a169 = 13<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">9<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a9 = 3<\/td>\n<td style=\"border: 1px solid #0F2742;\">196<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a196 = 14<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">16<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a16 = 4<\/td>\n<td style=\"border: 1px solid #0F2742;\">225<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a225 = 15<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">25<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a25 = 5<\/td>\n<td style=\"border: 1px solid #0F2742;\">256<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a256 = 16<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">36<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a36 = 6<\/td>\n<td style=\"border: 1px solid #0F2742;\">289<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a289 = 17<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">49<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a49 = 7<\/td>\n<td style=\"border: 1px solid #0F2742;\">324<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a324 = 18<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">64<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a64 = 8<\/td>\n<td style=\"border: 1px solid #0F2742;\">361<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a361 = 19<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">81<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a81 = 9<\/td>\n<td style=\"border: 1px solid #0F2742;\">400<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a400 = 20<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">100<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a100 = 10<\/td>\n<td style=\"border: 1px solid #0F2742;\">441<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a441 = 21<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"background: #FFF8EC; border-left: 6px solid #C77F0C; padding: 15px; margin: 20px 0; color: #0f2742;\"><strong>&#x1f4a1; Astuce :<\/strong> pour les multiples de 100, retirez les deux z\u00e9ros et ajoutez-en un \u00e0 la racine. \u221a400 = 20 car \u221a4 = 2. De m\u00eame, \u221a1 000 000 = 1 000. Attention, \u221a1 000 n\u2019est pas un entier : il faut un nombre pair de z\u00e9ros.<\/div>\n<h2 dir=\"ltr\">Quelle est la valeur de racine de 3 ?<\/h2>\n<p dir=\"ltr\"><strong>\u221a3 \u2248 1,732.<\/strong> C\u2019est un nombre <strong>irrationnel<\/strong> : il ne s\u2019\u00e9crit ni sous forme de fraction ni sous forme de nombre d\u00e9cimal, et ses d\u00e9cimales ne s\u2019arr\u00eatent jamais. On utilise donc une valeur approch\u00e9e, ou on garde l\u2019\u00e9criture \u221a3 pour obtenir un r\u00e9sultat exact.<\/p>\n<p dir=\"ltr\">Quelques calculs reviennent souvent :<\/p>\n<ul dir=\"ltr\">\n<li>(\u221a3)\u00b2 = 3 ;<\/li>\n<li>(2\u221a3)\u00b2 = 2\u00b2 \u00d7 3 = 12 ;<\/li>\n<li>\u221a3 \/ 2 \u2248 0,866 : c\u2019est la hauteur d\u2019un triangle \u00e9quilat\u00e9ral de c\u00f4t\u00e9 1 ;<\/li>\n<li>1 \/ \u221a3 = \u221a3 \/ 3 \u2248 0,577.<\/li>\n<\/ul>\n<p dir=\"ltr\">C\u2019est la m\u00eame chose pour \u221a2 et \u221a5. Voici les valeurs \u00e0 conna\u00eetre pour les nombres qui ne sont pas des carr\u00e9s parfaits :<\/p>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Racine<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Forme simplifi\u00e9e<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Valeur approch\u00e9e au milli\u00e8me<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a2<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a2<\/td>\n<td style=\"border: 1px solid #0F2742;\">1,414<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a3<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a3<\/td>\n<td style=\"border: 1px solid #0F2742;\">1,732<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a5<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a5<\/td>\n<td style=\"border: 1px solid #0F2742;\">2,236<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a6<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a6<\/td>\n<td style=\"border: 1px solid #0F2742;\">2,449<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a7<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a7<\/td>\n<td style=\"border: 1px solid #0F2742;\">2,646<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a8<\/td>\n<td style=\"border: 1px solid #0F2742;\">2\u221a2<\/td>\n<td style=\"border: 1px solid #0F2742;\">2,828<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a10<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a10<\/td>\n<td style=\"border: 1px solid #0F2742;\">3,162<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a12<\/td>\n<td style=\"border: 1px solid #0F2742;\">2\u221a3<\/td>\n<td style=\"border: 1px solid #0F2742;\">3,464<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a20<\/td>\n<td style=\"border: 1px solid #0F2742;\">2\u221a5<\/td>\n<td style=\"border: 1px solid #0F2742;\">4,472<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a50<\/td>\n<td style=\"border: 1px solid #0F2742;\">5\u221a2<\/td>\n<td style=\"border: 1px solid #0F2742;\">7,071<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<h2 dir=\"ltr\">Quelles sont les formules des racines carr\u00e9es ?<\/h2>\n<p dir=\"ltr\">Pour tous nombres <strong>a \u2265 0<\/strong> et <strong>b \u2265 0<\/strong> :<\/p>\n<ul dir=\"ltr\">\n<li><strong>(\u221aa)\u00b2 = a<\/strong> : (\u221a5)\u00b2 = 5.<\/li>\n<li><strong>\u221a(a\u00b2) = a<\/strong> : \u221a(6\u00b2) = 6. Si <em>a<\/em> peut \u00eatre n\u00e9gatif, on \u00e9crit \u221a(a\u00b2) = |a| (valeur absolue) : \u221a((\u22126)\u00b2) = \u221a36 = 6.<\/li>\n<li><strong>\u221a(a \u00d7 b) = \u221aa \u00d7 \u221ab<\/strong> : \u221a(4 \u00d7 9) = \u221a4 \u00d7 \u221a9 = 2 \u00d7 3 = 6.<\/li>\n<li><strong>\u221a(a \/ b) = \u221aa \/ \u221ab<\/strong>, avec <strong>b &gt; 0<\/strong> : \u221a(16\/49) = 4\/7.<\/li>\n<\/ul>\n<p dir=\"ltr\">Ces formules se combinent avec les identit\u00e9s remarquables. Exemple :<br \/>\n(2\u221a3 \u2212 3\u221a2)\u00b2 = (2\u221a3)\u00b2 \u2212 2 \u00d7 2\u221a3 \u00d7 3\u221a2 + (3\u221a2)\u00b2 = 12 \u2212 12\u221a6 + 18 = <strong>30 \u2212 12\u221a6<\/strong>.<\/p>\n<h3 dir=\"ltr\">Comment enlever une racine carr\u00e9e au d\u00e9nominateur ?<\/h3>\n<p dir=\"ltr\">On multiplie le num\u00e9rateur et le d\u00e9nominateur par la racine :<\/p>\n<ul dir=\"ltr\">\n<li>1 \/ \u221a2 = \u221a2 \/ (\u221a2 \u00d7 \u221a2) = <strong>\u221a2 \/ 2<\/strong> \u2248 0,707 ;<\/li>\n<li>6 \/ \u221a3 = 6\u221a3 \/ 3 = <strong>2\u221a3<\/strong>.<\/li>\n<\/ul>\n<p dir=\"ltr\">On obtient la m\u00eame valeur, \u00e9crite sans racine au d\u00e9nominateur. C\u2019est la forme attendue dans un r\u00e9sultat final.<\/p>\n<h3 dir=\"ltr\">Peut-on additionner des racines carr\u00e9es ?<\/h3>\n<p dir=\"ltr\">Pas en additionnant les nombres sous le radical. <strong>\u221aa + \u221ab n\u2019est pas \u00e9gal \u00e0 \u221a(a + b).<\/strong><\/p>\n<ul dir=\"ltr\">\n<li>\u221a9 + \u221a16 = 3 + 4 = 7<\/li>\n<li>\u221a(9 + 16) = \u221a25 = 5<\/li>\n<\/ul>\n<p dir=\"ltr\">En revanche, on peut regrouper les racines <strong>identiques<\/strong>, comme on regroupe des <em>x<\/em> en alg\u00e8bre : 3\u221a5 + 2\u221a5 = 5\u221a5. Pour 2\u221a3 + \u221a2, on ne peut pas simplifier davantage.<\/p>\n<div style=\"background: #FFF8EC; border-left: 6px solid #C77F0C; padding: 15px; margin: 20px 0; color: #0f2742;\"><strong>&#x1f4a1; Astuce :<\/strong> la racine se \u00ab partage \u00bb sur une multiplication ou une division, jamais sur une addition ou une soustraction. En cas de doute, testez avec 9 et 16 : le calcul vous montre tout de suite si la r\u00e8gle est fausse.<\/div>\n<h2 dir=\"ltr\">Comment calculer une racine carr\u00e9e ?<\/h2>\n<h3 dir=\"ltr\">Avec une calculatrice ou un tableur<\/h3>\n<p dir=\"ltr\">Utilisez la touche <strong>\u221a<\/strong>. Sur un tableur en fran\u00e7ais, la fonction s\u2019\u00e9crit =RACINE(A1). Dans les langages informatiques et sur les calculatrices anglophones, on trouve <strong>sqrt<\/strong>, pour <em>square root<\/em>.<\/p>\n<h3 dir=\"ltr\">Sans calculatrice, par encadrement<\/h3>\n<p dir=\"ltr\">Prenons \u221a20 :<\/p>\n<ol dir=\"ltr\">\n<li><strong>Cherchez les deux carr\u00e9s parfaits qui entourent le nombre<\/strong> : 16 &lt; 20 &lt; 25.<\/li>\n<li><strong>Prenez leurs racines<\/strong> : 4 &lt; \u221a20 &lt; 5.<\/li>\n<li><strong>Affinez au dixi\u00e8me<\/strong> en testant des d\u00e9cimaux : 4,4\u00b2 = 19,36 et 4,5\u00b2 = 20,25. Donc 4,4 &lt; \u221a20 &lt; 4,5.<\/li>\n<\/ol>\n<p dir=\"ltr\">Vous pouvez continuer au centi\u00e8me de la m\u00eame fa\u00e7on. La calculatrice donne \u221a20 \u2248 4,472.<\/p>\n<h3 dir=\"ltr\">En simplifiant la racine<\/h3>\n<p dir=\"ltr\">Simplifier une racine carr\u00e9e, c\u2019est l\u2019\u00e9crire sous la forme <strong>a\u221ab<\/strong> avec <em>b<\/em> le plus petit possible. On cherche dans le nombre le <strong>plus grand carr\u00e9 parfait<\/strong> qui le divise :<\/p>\n<ul dir=\"ltr\">\n<li>\u221a72 = \u221a(36 \u00d7 2) = 6\u221a2 ;<\/li>\n<li>\u221a48 = \u221a(16 \u00d7 3) = 4\u221a3 ;<\/li>\n<li>\u221a180 = \u221a(36 \u00d7 5) = 6\u221a5.<\/li>\n<\/ul>\n<div style=\"background: #FFF8EC; border-left: 6px solid #C77F0C; padding: 15px; margin: 20px 0; color: #0f2742;\"><strong>&#x1f4a1; Astuce :<\/strong> testez les carr\u00e9s parfaits dans l\u2019ordre d\u00e9croissant (100, 81, 64, 49, 36, 25, 16, 9, 4). Le premier qui divise le nombre donne directement la forme la plus simple. Si vous commencez par 4 pour \u221a72, vous devrez simplifier deux fois.<\/div>\n<\/div>\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"127774\" class=\"elementor elementor-127774\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-5a7b6a2a elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"5a7b6a2a\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-749af387 ae-bg-gallery-type-default\" data-id=\"749af387\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1b4ed465 elementor-widget elementor-widget-heading\" data-id=\"1b4ed465\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">COURS PARTICULIERS EN LIGNE<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-16d47760 elementor-widget elementor-widget-heading\" data-id=\"16d47760\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Nous avons s\u00e9lectionn\u00e9 pour vous les meilleurs professeurs particuliers.<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21a162bf elementor-widget elementor-widget-heading\" data-id=\"21a162bf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">POUR ACC\u00c9L\u00c9RER MA PROGRESSION<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5600477e elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"5600477e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-md\" href=\"https:\/\/groupe-reussite.fr\/cours-en-ligne\/toutes-matieres\/tous-niveaux\/france\/\" target=\"_blank\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours particuliers en ligne<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1c7a7876 elementor-widget elementor-widget-text-editor\" data-id=\"1c7a7876\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: left;\"><b>Avis Google France <\/b><span style=\"color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2aa12288 ae-bg-gallery-type-default\" data-id=\"2aa12288\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<h2 dir=\"ltr\">Comment \u00e9crire le symbole racine carr\u00e9e ?<\/h2>\n<p dir=\"ltr\">Le symbole s\u2019appelle le <strong>radical<\/strong> : \u221a. Pour le taper :<\/p>\n<ul dir=\"ltr\">\n<li>dans Word ou Google Docs, passez par l\u2019\u00e9diteur d\u2019\u00e9quations ou par le menu d\u2019insertion de caract\u00e8res sp\u00e9ciaux ;<\/li>\n<li>sous Windows, maintenez la touche Alt et tapez 251 sur le pav\u00e9 num\u00e9rique ;<\/li>\n<li>sur un clavier sans symbole, \u00e9crivez <strong>sqrt(3)<\/strong> ou <strong>3^(1\/2)<\/strong>, deux notations que comprennent les calculatrices et les tableurs.<\/li>\n<\/ul>\n<p dir=\"ltr\">\u00c0 la main, la barre du radical doit couvrir <strong>tout<\/strong> le nombre concern\u00e9. \u221a9 + 16 et \u221a(9 + 16) ne donnent pas le m\u00eame r\u00e9sultat.<\/p>\n<h2 dir=\"ltr\">Quelle diff\u00e9rence entre racine carr\u00e9e et racine cubique ?<\/h2>\n<p dir=\"ltr\">La <strong>racine cubique<\/strong> d\u2019un nombre, not\u00e9e \u221ba, est le nombre dont le <strong>cube<\/strong> vaut <em>a<\/em> : \u221b8 = 2 car 2\u00b3 = 2 \u00d7 2 \u00d7 2 = 8, et \u221b64 = 4 car 4\u00b3 = 64. Contrairement \u00e0 la racine carr\u00e9e, elle existe aussi pour les nombres n\u00e9gatifs : \u221b(\u221227) = \u22123.<\/p>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Confusion fr\u00e9quente<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Ce qu\u2019il faut retenir<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Racine carr\u00e9e \/ racine cubique<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a64 = 8 car 8\u00b2 = 64 ; \u221b64 = 4 car 4\u00b3 = 64<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221aa + \u221ab \/ \u221a(a + b)<\/td>\n<td style=\"border: 1px solid #0F2742;\">Ils ne sont pas \u00e9gaux : \u221a9 + \u221a16 = 7 et \u221a25 = 5<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">\u221a25 \/ solutions de x\u00b2 = 25<\/td>\n<td style=\"border: 1px solid #0F2742;\">\u221a25 = 5 seulement ; l\u2019\u00e9quation a deux solutions, 5 et \u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">(\u221aa)\u00b2 \/ \u221a(a\u00b2)<\/td>\n<td style=\"border: 1px solid #0F2742;\">(\u221aa)\u00b2 = a n\u2019a de sens que si a \u2265 0 ; \u221a(a\u00b2) = |a| pour tout a<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">2\u221a3 \/ \u221a(2 \u00d7 3)<\/td>\n<td style=\"border: 1px solid #0F2742;\">2\u221a3 = \u221a12 \u2248 3,464 alors que \u221a6 \u2248 2,449<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 dir=\"ltr\">\u00c0 quoi servent les racines carr\u00e9es en g\u00e9om\u00e9trie ?<\/h2>\n<p dir=\"ltr\">On retrouve les racines carr\u00e9es d\u00e8s qu\u2019on calcule une longueur avec le <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\">th\u00e9or\u00e8me de Pythagore<\/a>. Trois r\u00e9sultats reviennent souvent dans les <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\">figures g\u00e9om\u00e9triques<\/a> :<\/p>\n<table class=\"table\" style=\"width: 100%; border-color: #0F2742; color: #0f2742; background: #ffffff;\">\n<tbody>\n<tr>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Figure (c\u00f4t\u00e9 a)<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Longueur<\/strong><\/td>\n<td style=\"background: #0F2742; color: #ffffff; border: 1px solid #0F2742; text-align: left;\"><strong>Formule<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Carr\u00e9<\/td>\n<td style=\"border: 1px solid #0F2742;\">Diagonale<\/td>\n<td style=\"border: 1px solid #0F2742;\">a\u221a2<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Triangle \u00e9quilat\u00e9ral<\/td>\n<td style=\"border: 1px solid #0F2742;\">Hauteur<\/td>\n<td style=\"border: 1px solid #0F2742;\">a\u221a3 \/ 2<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #0F2742;\">Cube<\/td>\n<td style=\"border: 1px solid #0F2742;\">Grande diagonale<\/td>\n<td style=\"border: 1px solid #0F2742;\">a\u221a3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p dir=\"ltr\"><strong>Exemple 1 : le carr\u00e9.<\/strong> La diagonale d\u2019un carr\u00e9 mesure 7 cm. Son c\u00f4t\u00e9 vaut 7 \/ \u221a2 cm, donc son aire vaut (7 \/ \u221a2)\u00b2 = 49 \/ 2 = <strong>24,5 cm\u00b2<\/strong>.<\/p>\n<p dir=\"ltr\"><strong>Exemple 2 : le triangle \u00e9quilat\u00e9ral.<\/strong> Sa hauteur mesure 5 cm. On r\u00e9sout a\u221a3 \/ 2 = 5, donc a = 10 \/ \u221a3. Le p\u00e9rim\u00e8tre vaut 3 \u00d7 10 \/ \u221a3 = 30 \/ \u221a3 = <strong>10\u221a3 cm<\/strong>, soit environ 17,3 cm.<\/p>\n<p dir=\"ltr\"><strong>Exemple 3 : Pythagore.<\/strong> Le triangle EFG est rectangle en E, avec EF = 3\u221a2 cm et FG = 6\u221a5 cm. L\u2019hypot\u00e9nuse est [FG], donc :<br \/>\nEG\u00b2 = FG\u00b2 \u2212 EF\u00b2 = (6\u221a5)\u00b2 \u2212 (3\u221a2)\u00b2 = 180 \u2212 18 = 162.<br \/>\nEG = \u221a162 = \u221a(81 \u00d7 2) = <strong>9\u221a2 cm<\/strong>.<\/p>\n<p dir=\"ltr\">Pour vous entra\u00eener, retrouvez nos <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-racines-carrees\/\">exercices corrig\u00e9s sur les racines carr\u00e9es<\/a>.<\/p>\n<p dir=\"ltr\">Pour consolider le calcul avec les racines, les puissances et les fractions, les <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\">cours particuliers de maths<\/a> peuvent vous aider. Avec un enseignant, vous pourrez :<\/p>\n<ul dir=\"ltr\">\n<li>revoir la d\u00e9finition et les formules jusqu\u2019\u00e0 les appliquer sans h\u00e9siter ;<\/li>\n<li>vous entra\u00eener \u00e0 simplifier et \u00e0 rendre des r\u00e9sultats sous forme exacte ;<\/li>\n<li>pr\u00e9parer les exercices de g\u00e9om\u00e9trie du brevet ou les calculs de seconde.<\/li>\n<\/ul>\n<h2 dir=\"ltr\">FAQ : questions fr\u00e9quentes sur les racines carr\u00e9es<\/h2>\n        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Quelle est la racine carr\u00e9e de 100 ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tLa racine carr\u00e9e de 100 est 10, car 10 \u00d7 10 = 100. C\u2019est un carr\u00e9 parfait, comme 64 (racine 8), 121 (racine 11) ou 144 (racine 12).                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Quelle est la racine carr\u00e9e de 0 ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tLa racine carr\u00e9e de 0 est 0, car 0 \u00d7 0 = 0. Avec 1, c\u2019est le seul nombre \u00e9gal \u00e0 sa racine carr\u00e9e.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Peut-on calculer la racine carr\u00e9e d\u2019un nombre n\u00e9gatif ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tNon, pas avec les nombres r\u00e9els \u00e9tudi\u00e9s au coll\u00e8ge et au lyc\u00e9e : un carr\u00e9 est toujours positif ou nul, donc aucun r\u00e9el au carr\u00e9 ne donne \u22121 ou \u22129. La calculatrice affiche une erreur.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>La racine carr\u00e9e d\u2019un nombre est-elle toujours plus petite que lui ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tSeulement pour les nombres sup\u00e9rieurs \u00e0 1 : \u221a100 = 10. Entre 0 et 1, c\u2019est l\u2019inverse : \u221a0,25 = 0,5, qui est plus grand que 0,25.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>Comment savoir si un nombre est un carr\u00e9 parfait ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tCherchez un entier dont le carr\u00e9 donne ce nombre. Un carr\u00e9 parfait se termine toujours par 0, 1, 4, 5, 6 ou 9 : un nombre qui finit par 2, 3, 7 ou 8 n\u2019en est jamais un.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t        <section class=\"sc_fs_faq sc_card \">\n            <div>\n\t\t\t\t<h3>En quelle classe \u00e9tudie-t-on les racines carr\u00e9es ?<\/h3>                <div>\n\t\t\t\t\t                    <p>\n\t\t\t\t\t\tLa d\u00e9finition et l\u2019encadrement d\u2019une racine carr\u00e9e entre deux entiers figurent au programme du cycle 4, au coll\u00e8ge. En seconde, on d\u00e9montre la formule \u221a(ab) = \u221aa \u00d7 \u221ab et on calcule avec des racines carr\u00e9es.                    <\/p>\n                <\/div>\n            <\/div>\n        <\/section>\n\t\t\n<script type=\"application\/ld+json\">\n    {\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Quelle est la racine carr\u00e9e de 100 ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"La racine carr\u00e9e de 100 est 10, car 10 \u00d7 10 = 100. C\u2019est un carr\u00e9 parfait, comme 64 (racine 8), 121 (racine 11) ou 144 (racine 12).\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Quelle est la racine carr\u00e9e de 0 ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"La racine carr\u00e9e de 0 est 0, car 0 \u00d7 0 = 0. Avec 1, c\u2019est le seul nombre \u00e9gal \u00e0 sa racine carr\u00e9e.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Peut-on calculer la racine carr\u00e9e d\u2019un nombre n\u00e9gatif ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Non, pas avec les nombres r\u00e9els \u00e9tudi\u00e9s au coll\u00e8ge et au lyc\u00e9e : un carr\u00e9 est toujours positif ou nul, donc aucun r\u00e9el au carr\u00e9 ne donne \u22121 ou \u22129. La calculatrice affiche une erreur.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"La racine carr\u00e9e d\u2019un nombre est-elle toujours plus petite que lui ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Seulement pour les nombres sup\u00e9rieurs \u00e0 1 : \u221a100 = 10. Entre 0 et 1, c\u2019est l\u2019inverse : \u221a0,25 = 0,5, qui est plus grand que 0,25.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Comment savoir si un nombre est un carr\u00e9 parfait ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Cherchez un entier dont le carr\u00e9 donne ce nombre. Un carr\u00e9 parfait se termine toujours par 0, 1, 4, 5, 6 ou 9 : un nombre qui finit par 2, 3, 7 ou 8 n\u2019en est jamais un.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"En quelle classe \u00e9tudie-t-on les racines carr\u00e9es ?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"La d\u00e9finition et l\u2019encadrement d\u2019une racine carr\u00e9e entre deux entiers figurent au programme du cycle 4, au coll\u00e8ge. En seconde, on d\u00e9montre la formule \u221a(ab) = \u221aa \u00d7 \u221ab et on calcule avec des racines carr\u00e9es.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t    ]\n}\n<\/script>\n\n<h2 dir=\"ltr\"><strong>Sources<\/strong><\/h2>\n<ul dir=\"ltr\">\n<li>Minist\u00e8re de l\u2019\u00c9ducation nationale, <em>Programme de math\u00e9matiques de seconde g\u00e9n\u00e9rale et technologique<\/em>, annexe (partie \u00ab Utiliser le calcul litt\u00e9ral \u00bb)<\/li>\n<li>Acad\u00e9mie de Bordeaux, <em>Programme cycle 4 : objectifs d\u2019apprentissage<\/em>, partie \u00ab Racine carr\u00e9e \u00bb, 2026<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Voici quelques autres notions et chapitres de maths qu\u2019il faut absolument conna\u00eetre pour r\u00e9ussir au sous-test 2 du Tage Mage :<\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/\">Cours en ligne sur les fractions au Tage Mage<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pourcentages\/\">R\u00e9sum\u00e9 de cours sur les pourcentages au sous-test 2 du Tage Mage<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-algebre\/\">Fiche de r\u00e9vision sur l\u2019alg\u00e8bre au Tage Mage<\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-figures-geometriques\/\">Cours en ligne sur la g\u00e9om\u00e9trie au sous-test 2 du Tage Mage<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-vitesse\/\">Comprendre la vitesse en calcul au Tage Mage<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-fractions\/\">Exercices sur les fractions au Tage Mage<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-pourcentages\/\">Exercices corrig\u00e9s sur les pourcentages au sous-test 2 du Tage Mage<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau Par Seda Biber, mis \u00e0 jour le 17\/10\/2026 La racine carr\u00e9e d\u2019un nombre positif a, not\u00e9e \u221aa, est le nombre positif dont le carr\u00e9 est \u00e9gal \u00e0 a. Par exemple, \u221a9 = 3 car 3\u00b2 = 9, et \u221a100 = 10 car 10\u00b2 = 100. Quand le [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ocean_post_layout":"full-screen","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"ressource","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"on","ocean_disable_heading":"on","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"on","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-53590","page","type-page","status-publish","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau<\/title>\n<meta name=\"description\" content=\"Racine carr\u00e9e d\u2019un nombre : d\u00e9finition, formules, tableau des racines de 0 \u00e0 441, valeur de racine de 3, simplification et calcul.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau\" \/>\n<meta property=\"og:description\" content=\"Racine carr\u00e9e d\u2019un nombre : d\u00e9finition, formules, tableau des racines de 0 \u00e0 441, valeur de racine de 3, simplification et calcul.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\" \/>\n<meta property=\"og:site_name\" content=\"Groupe R\u00e9ussite\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/\" \/>\n<meta property=\"article:modified_time\" content=\"2026-10-17T11:54:04+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png\" \/>\n\t<meta property=\"og:image:width\" content=\"170\" \/>\n\t<meta property=\"og:image:height\" content=\"180\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@GroupeReussite\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/cours-en-ligne-racines-carrees\\\/\",\"url\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/cours-en-ligne-racines-carrees\\\/\",\"name\":\"Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/#website\"},\"datePublished\":\"2020-06-11T13:30:26+00:00\",\"dateModified\":\"2026-10-17T11:54:04+00:00\",\"description\":\"Racine carr\u00e9e d\u2019un nombre : d\u00e9finition, formules, tableau des racines de 0 \u00e0 441, valeur de racine de 3, simplification et calcul.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/cours-en-ligne-racines-carrees\\\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/cours-en-ligne-racines-carrees\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/cours-en-ligne-racines-carrees\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Cours sur les racines carr\u00e9es\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/#website\",\"url\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/\",\"name\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\",\"description\":\"Stage et Cours particuliers maths, fran\u00e7ais, anglais, informatique, physique chimie\",\"publisher\":{\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/#organization\",\"name\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\",\"url\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/wp-content\\\/uploads\\\/2026\\\/05\\\/logo-groupe-reussite-carre.png\",\"contentUrl\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/wp-content\\\/uploads\\\/2026\\\/05\\\/logo-groupe-reussite-carre.png\",\"width\":170,\"height\":180,\"caption\":\"Groupe R\u00e9ussite - Cours particuliers et stages de vacances\"},\"image\":{\"@id\":\"https:\\\/\\\/groupe-reussite.fr\\\/ressources\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/GroupeReussiteOfficiel\\\/\",\"https:\\\/\\\/x.com\\\/GroupeReussite\",\"https:\\\/\\\/www.youtube.com\\\/c\\\/GroupeReussite\",\"https:\\\/\\\/www.instagram.com\\\/groupe_reussite_officiel\\\/\",\"https:\\\/\\\/fr.linkedin.com\\\/company\\\/groupe-reussite\",\"https:\\\/\\\/www.tiktok.com\\\/@groupereussite\",\"https:\\\/\\\/fr.pinterest.com\\\/GroupeReussite\\\/\",\"https:\\\/\\\/www.reddit.com\\\/user\\\/Groupe-Reussite\\\/\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau","description":"Racine carr\u00e9e d\u2019un nombre : d\u00e9finition, formules, tableau des racines de 0 \u00e0 441, valeur de racine de 3, simplification et calcul.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/","og_locale":"fr_FR","og_type":"article","og_title":"Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau","og_description":"Racine carr\u00e9e d\u2019un nombre : d\u00e9finition, formules, tableau des racines de 0 \u00e0 441, valeur de racine de 3, simplification et calcul.","og_url":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/","og_site_name":"Groupe R\u00e9ussite","article_publisher":"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/","article_modified_time":"2026-10-17T11:54:04+00:00","og_image":[{"width":170,"height":180,"url":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_site":"@GroupeReussite","twitter_misc":{"Dur\u00e9e de lecture estim\u00e9e":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/","url":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/","name":"Racine carr\u00e9e : d\u00e9finition, formules, calcul et tableau","isPartOf":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#website"},"datePublished":"2020-06-11T13:30:26+00:00","dateModified":"2026-10-17T11:54:04+00:00","description":"Racine carr\u00e9e d\u2019un nombre : d\u00e9finition, formules, tableau des racines de 0 \u00e0 441, valeur de racine de 3, simplification et calcul.","breadcrumb":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/groupe-reussite.fr\/ressources\/"},{"@type":"ListItem","position":2,"name":"Cours sur les racines carr\u00e9es"}]},{"@type":"WebSite","@id":"https:\/\/groupe-reussite.fr\/ressources\/#website","url":"https:\/\/groupe-reussite.fr\/ressources\/","name":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances","description":"Stage et Cours particuliers maths, fran\u00e7ais, anglais, informatique, physique chimie","publisher":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/groupe-reussite.fr\/ressources\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Organization","@id":"https:\/\/groupe-reussite.fr\/ressources\/#organization","name":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances","url":"https:\/\/groupe-reussite.fr\/ressources\/","logo":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/","url":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","contentUrl":"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2026\/05\/logo-groupe-reussite-carre.png","width":170,"height":180,"caption":"Groupe R\u00e9ussite - Cours particuliers et stages de vacances"},"image":{"@id":"https:\/\/groupe-reussite.fr\/ressources\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/","https:\/\/x.com\/GroupeReussite","https:\/\/www.youtube.com\/c\/GroupeReussite","https:\/\/www.instagram.com\/groupe_reussite_officiel\/","https:\/\/fr.linkedin.com\/company\/groupe-reussite","https:\/\/www.tiktok.com\/@groupereussite","https:\/\/fr.pinterest.com\/GroupeReussite\/","https:\/\/www.reddit.com\/user\/Groupe-Reussite\/"]}]}},"_links":{"self":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/53590","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/comments?post=53590"}],"version-history":[{"count":4,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/53590\/revisions"}],"predecessor-version":[{"id":279771,"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/pages\/53590\/revisions\/279771"}],"wp:attachment":[{"href":"https:\/\/groupe-reussite.fr\/ressources\/wp-json\/wp\/v2\/media?parent=53590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}