{"id":362,"date":"2017-11-08T20:00:59","date_gmt":"2017-11-08T11:00:59","guid":{"rendered":"http:\/\/tokiensis.com\/cahier\/?p=362"},"modified":"2017-11-03T10:01:38","modified_gmt":"2017-11-03T01:01:38","slug":"french-math-003","status":"publish","type":"post","link":"https:\/\/tokiensis.com\/cahier\/french-math-003\/","title":{"rendered":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff13\uff09Racines carr\u00e9es et puissance"},"content":{"rendered":"<p>\u5e73\u65b9\u6839\u3068\u4e57\u6570\u306e\u30ce\u30fc\u30c8<\/p>\n<h3>Soit\u00a0\u200b<span class=\"math inherit-color \">\\( a \\)<\/span>\u200b un nombre positif.<\/h3>\n<p>\u6b63\u306e\u6570 \u200b<span class=\"math inherit-color \">\\( a \\)<\/span>\u200b \u304c\u3042\u308b\u3082\u306e\u3068\u3059\u308b\u3002<\/p>\n<h3>La racine carr\u00e9e du nombre positif\u00a0\u200b<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b est le nombre positif dont le carr\u00e9 est \u00e9gal \u00e0\u00a0\u200b<span class=\"math inherit-color \">\\( a \\)<\/span>\u200b.<\/h3>\n<p>\u6b63\u306e\u6570 \u200b<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b \u306e\u5e73\u65b9\u6839\u306f\u00a0\u305d\u306e2\u4e57\u304c<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b\u3068\u7b49\u3057\u3044\u6b63\u306e\u6570\u3067\u3042\u308b\u3002<\/p>\n<ul>\n<li><strong>racine carr\u00e9e<\/strong> \u5e73\u65b9\u6839<\/li>\n<li><strong>carr\u00e9<\/strong> 2\u4e57<\/li>\n<\/ul>\n<h3>On le note\u00a0\u200b<span class=\"math inherit-color\">\\( \\sqrt{a} \\)<\/span>\u200b.<\/h3>\n<p>\u3053\u308c\u3092 \u200b<span class=\"math inherit-color\">\\( \\sqrt{a} \\)<\/span>\u200b\u3068\u66f8\u304f\u3002<\/p>\n<h3>Quel que soit le nombre positif\u00a0\u200b<span class=\"math inherit-color \">\\( a \\)<\/span>\u200b :<\/h3>\n<p>\u4efb\u610f\u306e\u6b63\u306e\u6570 \u200b<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b\u306b\u3064\u3044\u3066\uff08\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\uff09 :<\/p>\n<h4 style=\"text-align: left;\">\u200b<span class=\"math inherit-color\">\\( (\\sqrt{a})^2=a \\)<\/span>\u200b et \u00a0\u200b<span class=\"math inherit-color\">\\( \\sqrt{a^2} = a \\)<\/span>\u200b<\/h4>\n<p style=\"text-align: left;\">\u200b<span class=\"math inherit-color\">\\( (\\sqrt{a})^2=a \\)<\/span>\u00a0\u304b\u3064 \u200b<span class=\"math inherit-color\">\\( \\sqrt{a^2} = a \\)<\/span>\u200b<\/p>\n<h3>Attention ! : En g\u00e9n\u00e9ral\u00a0\u200b<span class=\"math inherit-color \">\\( \\sqrt{a+b} \\neq \\sqrt{a} + \\sqrt{b} \\)<\/span>\u200b.<\/h3>\n<p>\u6ce8\u610f\uff01 : \u4e00\u822c\u7684\u306b \u200b<span class=\"math inherit-color \">\\( \\sqrt{a+b} \\neq \\sqrt{a} + \\sqrt{b} \\)<\/span>\u200b \u3067\u3042\u308b\u3002<\/p>\n<h3>Soient\u00a0\u200b<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b un nombre non nul et\u00a0\u200b<span class=\"math inherit-color\">\\( n \\)<\/span>\u200b un entier naturel positif.<\/h3>\n<p>0\u3067\u306a\u3044\u6570\u5b57\u00a0\u200b<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b\u3068\u6b63\u306e\u81ea\u7136\u6570\u00a0\u200b<span class=\"math inherit-color\">\\( n \\)<\/span>\u200b\u304c\u3042\u308b\u3082\u306e\u3068\u3059\u308b\u3002<\/p>\n<h3>Le produit de \u200b<span class=\"math inherit-color\">\\( n \\)<\/span>\u200b\u00a0facteurs \u00e9gaux \u00e0\u00a0\u200b<span class=\"math inherit-color \">\\( a \\)<\/span>\u200b se note\u00a0\u200b<span class=\"math inherit-color\">\\( a^n \\)<\/span>\u200b:<\/h3>\n<p>\u200b<span class=\"math inherit-color\">\\( a \\)<\/span>\u200b\u306e\u00a0\u200b<span class=\"math inherit-color\">\\( n \\)<\/span>\u200b \u56de\u5206\u306e\u7a4d\u306f \u200b<span class=\"math inherit-color\">\\( a^n \\)<\/span>\u200b\u3068\u66f8\u304f:<\/p>\n<h4>\u200b<span class=\"math inherit-color \">\\( a^n = a \\times a \\times &#8230; \\times a \\)<\/span>\u200b,\u00a0\u200b<span class=\"math inherit-color\">\\( n \\)<\/span>\u200b fois.<\/h4>\n<p style=\"text-align: left;\">\u200b<span class=\"math inherit-color\">\\( a^n = a \\times a \\times &#8230; \\times a \\)<\/span>\u200b,\u00a0\u200b<span class=\"math inherit-color \">\\( n \\)<\/span>\u200b \u56de<\/p>\n<ul>\n<li><strong>le produit de <em>n<\/em> facteurs \u00e9gaux \u00e0 <em>a<\/em>\u00a0<\/strong>\u00a0a\u306b\u7b49\u3057\u3044\u6570\u306b\u5bfe\u3057\u3066\u306e\u4fc2\u6570 n\u306e\u7a4d = a\u3092n\u56de\u639b\u3051\u305f\u7d50\u679c<\/li>\n<\/ul>\n<h3>\u200b<span class=\"math inherit-color\">\\( a^{-1} \\)<\/span>\u200best l&#8217;inverse de\u00a0\u200b<span class=\"math inherit-color \">\\( a^n \\)<\/span>\u200b. Donc\u00a0\u200b<span class=\"math inherit-color _focus\">\\( a^{-1} = \\frac{1}{a^n} \\)<\/span> .<\/h3>\n<p><span class=\"math inherit-color\">\\( a^{-1} \\)<\/span>\u200b\u306f \u200b<span class=\"math inherit-color\">\\( a^n \\)<\/span>\u200b\u306e\u9006\u6570\u3067\u3042\u308b\u3002\u3064\u307e\u308a \u200b<span class=\"math inherit-color\">\\( a^{-1} = \\frac{1}{a^n} \\)<\/span><\/p>\n<h3>Notation scientifique normalis\u00e9e<\/h3>\n<p>\u6b63\u898f\u5316\u3055\u308c\u305f\u6307\u6570\u8868\u8a18<\/p>\n<h3>Tout nombre positif\u00a0\u200b<span class=\"math inherit-color \">\\( x \\)<\/span>\u200b peut s&#8217;\u00e9crire sous la forme :<\/h3>\n<p>\u3059\u3079\u3066\u306e\u6b63\u306e\u6570\u200b<span class=\"math inherit-color\">\\( x \\)<\/span>\u200b \u306f\u4ee5\u4e0b\u306e\u5f62\u5f0f\u3067\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b :<\/p>\n<h4 style=\"text-align: left;\">\u200b<span class=\"math inherit-color\">\\( x = a \\times 10^n \\)<\/span>\u200b, o\u00f9\u00a0\u200b<span class=\"math inherit-color \">\\( 1 \\leq a &lt; 10 \\)<\/span>\u200b et\u00a0\u200b<span class=\"math inherit-color \">\\( n \\)<\/span>\u200b est un entier relatif.<\/h4>\n<p>\u200b<span class=\"math inherit-color \">\\( x = a \\times 10^n \\)<\/span>\u200b\u3001 \u305f\u3060\u3057 \u200b<span class=\"math inherit-color \">\\( 1 \\leq a &lt; 10 \\)<\/span>\u200b\u304b\u3064 \u200b<span class=\"math inherit-color\">\\( n \\)<\/span>\u200b \u306f\u6574\u6570\u3067\u3042\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5e73\u65b9\u6839\u3068\u4e57\u6570\u306e\u30ce\u30fc\u30c8 Soit\u00a0\u200b\\( a \\)\u200b un nombre positif. \u6b63\u306e\u6570 \u200b\\( a \\)\u200b \u304c\u3042\u308b\u3082\u306e\u3068\u3059\u308b\u3002 La racine carr\u00e9e du nombre positif\u00a0\u200b\\( a  &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/tokiensis.com\/cahier\/french-math-003\/\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff13\uff09Racines carr\u00e9es et puissance&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[51],"tags":[32],"jetpack_publicize_connections":[],"aioseo_notices":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9fXRE-5Q","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":319,"url":"https:\/\/tokiensis.com\/cahier\/french-math-002\/","url_meta":{"origin":362,"position":0},"title":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff12\uff09Arithm\u00e9tique","date":"2017\u5e7411\u67082\u65e5","format":false,"excerpt":"\u516c\u7d04\u6570\u3001\u7d20\u6570\u3001\u65e2\u7d04\u5206\u6570\u306a\u3069\u306e\u30e1\u30e2 L'entier naturel non nul\u00a0m est un\u2026","rel":"","context":"\u30d5\u30e9\u30f3\u30b9\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":307,"url":"https:\/\/tokiensis.com\/cahier\/french-math-001\/","url_meta":{"origin":362,"position":1},"title":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u6570\u5b66\uff08\uff11\uff09Calculs sur les fractions","date":"2017\u5e7410\u670831\u65e5","format":false,"excerpt":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u3067\u5206\u6570\u306e\u8a08\u7b97\u3092\u5b66\u7fd2\u3057\u305f\u3068\u304d\u306e\u30ce\u30fc\u30c8 Pour additionner (ou soustr\u2026","rel":"","context":"\u30d5\u30e9\u30f3\u30b9\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":471,"url":"https:\/\/tokiensis.com\/cahier\/french-accords-des-participes-passes\/","url_meta":{"origin":362,"position":2},"title":"\u30d5\u30e9\u30f3\u30b9\u8a9e\uff1a\u904e\u53bb\u5206\u8a5e\u306e\u6027\u6570\u4e00\u81f4","date":"2018\u5e7412\u670822\u65e5","format":false,"excerpt":"\u81ea\u52d5\u8a5e\u3068\u4ed6\u52d5\u8a5e\u3067\u306e\u904e\u53bb\u5206\u8a5e\u306e\u6027\u6570\u4e00\u81f4\u306e\u307e\u3068\u3081\u3002\u6027\u6570\u5909\u5316\u3059\u308b\u5834\u5408\u306f\u8d64\u3001\u3057\u306a\u3044\u5834\u5408\u306f\u9752 \u00eatre\u3068\u4e00\u7dd2\u306b\u2026","rel":"","context":"\u30d5\u30e9\u30f3\u30b9\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":250,"url":"https:\/\/tokiensis.com\/cahier\/italiano-001\/","url_meta":{"origin":362,"position":3},"title":"\u30a4\u30bf\u30ea\u30a2\u8a9e\uff08\uff11\uff09L&#8217;Italia \u00e8 bella","date":"2017\u5e7410\u670823\u65e5","format":false,"excerpt":"L'uomo \u00e8 italiano. \u305d\u306e\u7537\u6027\u306f\u30a4\u30bf\u30ea\u30a2\u4eba\u3067\u3059\u3002 La donna non \u00e8 it\u2026","rel":"","context":"\u30a4\u30bf\u30ea\u30a2\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":104,"url":"https:\/\/tokiensis.com\/cahier\/memento-german-01\/","url_meta":{"origin":362,"position":4},"title":"\u30c9\u30a4\u30c4\u8a9e\u6587\u6cd5\u306e\u307e\u3068\u3081\uff08\uff11\uff09","date":"2017\u5e7410\u67083\u65e5","format":false,"excerpt":"\u6027\u6570\u5909\u5316\u306b\u3064\u3044\u3066 \u30c9\u30a4\u30c4\u8a9e\u306b\u306f\u7537\u6027\u3001\u4e2d\u6027\u3001\u5973\u6027\u306e\u5909\u5316\u304c\u3042\u308a\u3001\u8f9e\u66f8\u3067\u306f\u305d\u308c\u305e\u308c\u5b9a\u51a0\u8a5eder, das,\u2026","rel":"","context":"\u30c9\u30a4\u30c4\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":272,"url":"https:\/\/tokiensis.com\/cahier\/french-verb-01\/","url_meta":{"origin":362,"position":5},"title":"\u30d5\u30e9\u30f3\u30b9\u8a9e\uff1a\u00eatre\u3068avoir\u306e\u52d5\u8a5e\u5909\u5316\u306e\u307e\u3068\u3081","date":"2017\u5e7410\u670825\u65e5","format":false,"excerpt":"\u30d5\u30e9\u30f3\u30b9\u8a9e\u306e\u52d5\u8a5e\u00eatre\u300c\u301c\u3067\u3042\u308b\u300d\u3068avoir\u300c\u6301\u3063\u3066\u3044\u308b\u300d\u306f\u975e\u5e38\u306b\u3088\u304f\u4f7f\u308f\u308c\u308b\u306e\u3067\u4e0d\u898f\u5247\u52d5\u8a5e\u306a\u304c\u2026","rel":"","context":"\u30d5\u30e9\u30f3\u30b9\u8a9e","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts\/362"}],"collection":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/comments?post=362"}],"version-history":[{"count":3,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts\/362\/revisions"}],"predecessor-version":[{"id":375,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/posts\/362\/revisions\/375"}],"wp:attachment":[{"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/media?parent=362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/categories?post=362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tokiensis.com\/cahier\/wp-json\/wp\/v2\/tags?post=362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}