{"id":5868,"date":"2019-06-30T21:25:29","date_gmt":"2019-06-30T20:25:29","guid":{"rendered":"http:\/\/mathsguyon.fr\/?page_id=5868"},"modified":"2023-11-22T18:43:56","modified_gmt":"2023-11-22T17:43:56","slug":"racines-carrees","status":"publish","type":"page","link":"https:\/\/mathsguyon.fr\/?page_id=5868","title":{"rendered":"Racines carr\u00e9es"},"content":{"rendered":"

Cours<\/a> \u00a0\u00a0 \u00a0 Plan de travail avec corrig\u00e9s<\/a><\/h1>\n

Vid\u00e9os de cours :<\/span><\/strong><\/h1>\n

Vid\u00e9o<\/a> 1<\/strong> : D\u00e9finition + QCM n\u00b01<\/a><\/h2>\n

Vid\u00e9o 2<\/strong><\/a> :Les carr\u00e9s parfaits + QCM n\u00b02<\/a><\/h2>\n

Vid\u00e9o 3 :<\/strong><\/a>Propri\u00e9t\u00e9s des racines carr\u00e9es +\u00a0QCM n\u00b03<\/a><\/h2>\n

Vid\u00e9o\u00a0 : D\u00e9monstration fondamentale : <\/span><\/span><\/strong><\/a>$Pour~a\\geqslant 0~~et~~b\\geqslant 0~~, on ~a \\sqrt{a\\times b}=\\sqrt a \\times \\sqrt b$<\/span><\/h2>\n

Vid\u00e9o 4 : <\/strong><\/a>Racine carr\u00e9e et sommes + QCM n\u00b04<\/a><\/h2>\n

Vid\u00e9o\u00a0 : D\u00e9monstration fondamentale<\/span><\/strong><\/a> : <\/span><\/strong>Pour $a \\geqslant 0 ~\\text{et} b\\geqslant 0, \\text{on a} \\sqrt{a + b}\\leqslant\\sqrt{a} + \\sqrt{b}$<\/h2>\n

Vid\u00e9o 5\u00a0 <\/strong><\/a>: Mettre une somme sous la forme $a \\sqrt b$ + QCM n\u00b05<\/a><\/h2>\n

Vid\u00e9o 6<\/strong> <\/a>: R\u00e9duire une somme de racines carr\u00e9es+ QCM n\u00b06<\/a><\/h2>\n

Vid\u00e9o 7<\/strong><\/a> : Rendre un d\u00e9nominateur entier + QCM n\u00b07<\/a><\/h2>\n

Vid\u00e9o 8<\/a> : <\/strong>Quantit\u00e9 conjugu\u00e9e (facultatif)<\/h2>\n

Exercices d’application corrig\u00e9s en vid\u00e9o :<\/span><\/strong><\/h2>\n

D\u00e9finition :<\/strong><\/span><\/h2>\n

1. Simplifier l’\u00e9criture de<\/strong> : $A=\\sqrt {13^{2}}~~B=\\sqrt(-7)^{2}~~C=\\sqrt{121}~~D=\\sqrt{\\dfrac{4}{9}}$<\/p>\n

$E=(2\\sqrt {7})^{2}~~~F=\\sqrt(9)+3~~~G=\\sqrt{(3-7)^{2}}$ Correction<\/a><\/p>\n

2. Dire si les nombres suivants existent, et si oui, simplifier leur expression :<\/strong><\/p>\n

$\\sqrt {2^{3}}~~~(2\\sqrt3)^{2}~~~\\sqrt{(-2)^{2}}~~~(\\sqrt{-2})^{2}$<\/p>\n

Peut-on dire $\\sqrt2=1,4142~~ou~~\\sqrt2=1,41421356237$ Correction<\/a><\/p>\n

3. Simplifier, s’ils existent, les nombres suivants :<\/strong><\/p>\n

$\\sqrt{(-2)^{2}}~~;~~\\sqrt{-4^{2}}~~;~~-\\sqrt{4^{2}}~~;~~\\left(\\sqrt{-4}\\right)^{2} $ Correction<\/a><\/p>\n

$\\left(\\sqrt{4}\\right)^{2}~~;~~\\left(\\sqrt{7}\\right)^{2}~~;~~\\sqrt{7}~^{2}$\u00a0 Correction<\/a><\/p>\n

$\\sqrt{(-3)^{2}}~~;~~\\sqrt{-3^{2}}~~;~~\\left(-\\sqrt{3}\\right)~^{2}~~;~~\\sqrt \\pi ~~;~~\\sqrt{\\pi – 4}$\u00a0 Correction<\/a><\/p>\n

Propri\u00e9t\u00e9s des racines carr\u00e9es :<\/strong><\/span><\/h2>\n

1. Simplifier l’\u00e9criture de :<\/strong> $B=\\dfrac{\\sqrt{15}}{\\sqrt {27}}~~, ~~C=\\sqrt{25+144}~~ et ~~D=3\\sqrt{15} \\times 2 \\sqrt {20}$ Correction<\/a><\/p>\n

2. Simplifier l’\u00e9criture de<\/strong> : $A=\\sqrt{3}\\times \\sqrt {12}~~B=\\sqrt{5}\\times\\sqrt {45}~~, ~~C=\\dfrac{\\sqrt{48}}{\\sqrt{3}}~~ et ~~D=4\\sqrt{75} \\times\u00a0 \\sqrt {3}$ Correction<\/a><\/p>\n

Distributivit\u00e9 avec les racines carr\u00e9es :<\/strong><\/span><\/h2>\n

1. Simplifier l’\u00e9criture de<\/strong> : $-\\sqrt{5}(4-\\sqrt 5)$ puis de $ (\\sqrt 6 +1)(5-2\\sqrt6)$\u00a0 Correction<\/a><\/p>\n

2. Simplifier l’\u00e9criture de :<\/strong> $\\sqrt{2}(2-3\\sqrt 2)$\u00a0\u00a0 Correction<\/a><\/p>\n

3. Simplifier l’\u00e9criture de :<\/strong> $(3\\sqrt{2}+5)(\\sqrt 2-3)$\u00a0 Correction<\/a><\/p>\n

3. Simplifier l’\u00e9criture de :<\/strong> $(4+5\\sqrt{2})(2-3\\sqrt 2)$\u00a0 Correction<\/a><\/p>\n

4.\u00a0 Simplifier l’\u00e9criture de :<\/strong> $(5+\\sqrt 2)^{2}~~;~~(3-2\\sqrt 5)^{2}~~;~~(2-\\sqrt 3)(2+\\sqrt 3)$ \u00a0Correction<\/a><\/p>\n

Rendre entier un d\u00e9nominateur :<\/strong><\/span><\/h2>\n

$\\dfrac{2}{\\sqrt3}~~ et ~~\\dfrac{8}{3\\sqrt2}$ Correction<\/a><\/p>\n

Simplifier une racine carr\u00e9e :<\/strong><\/span><\/h2>\n

$A=\\sqrt{125}~~~B=4\\sqrt{80}~~~ et~~ C=-2\\sqrt{98}$\u00a0 Correction<\/a><\/p>\n

Somme de racines carr\u00e9es :<\/strong><\/span><\/h2>\n

$B=3\\sqrt5+5\\sqrt2-7\\sqrt5-2\\sqrt2$ Correction<\/a><\/p>\n

\u00c9crire sous la forme $a \\sqrt b$ :<\/strong><\/span><\/h2>\n

$A=4\\sqrt{18}-2 \\sqrt2$ Correction<\/a><\/p>\n

$A=7\\sqrt{24}+10\\sqrt{54}-2\\sqrt{150}$\u00a0 Correction<\/a><\/p>\n

$B=\\sqrt{12}+2\\sqrt{75}-2\\sqrt{300}$\u00a0 Correction<\/a><\/p>\n

$B=\\sqrt{75}+4\\sqrt{27}-5\\sqrt{48}$\u00a0 Correction<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Cours \u00a0\u00a0 \u00a0 Plan de travail avec corrig\u00e9s Vid\u00e9os de cours : Vid\u00e9o 1 : D\u00e9finition + QCM n\u00b01 Vid\u00e9o 2 :Les carr\u00e9s parfaits + QCM n\u00b02 Vid\u00e9o 3 :Propri\u00e9t\u00e9s des racines carr\u00e9es +\u00a0QCM n\u00b03 Vid\u00e9o\u00a0 : D\u00e9monstration fondamentale : … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":21,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5868","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5868","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5868"}],"version-history":[{"count":97,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5868\/revisions"}],"predecessor-version":[{"id":9395,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5868\/revisions\/9395"}],"up":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/21"}],"wp:attachment":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5868"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}