{"id":72774,"date":"2017-02-23T22:28:06","date_gmt":"2017-02-24T01:28:06","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=72774"},"modified":"2023-04-06T01:42:56","modified_gmt":"2023-04-06T04:42:56","slug":"problema-expressao-radical","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-expressao-radical\/","title":{"rendered":".Problema:  Express\u00e3o Radical"},"content":{"rendered":"<p style=\"margin:20px\">\n<div class=\"g1n\" style=\"line-height:25px;\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 9\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nSimplifique a express\u00e3o [tex]\\sqrt[n]{\\dfrac{600}{25^{n+2}-5^{2n+2}}}[\/tex].<\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\" style=\"line-height:35px;\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o <\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n[tex]<br \/>\n\\begin{align*}\\sqrt[n]{\\dfrac{600}{25^{n+2}-5^{2n+2}}}&#038; =\\sqrt[n]{\\dfrac{600}{25^{n+2}-(5^2)^{n+1}}} \\\\<br \/>\n&#038;=\\sqrt[n]{\\dfrac{600}{25^{n+2}-25^{n+1}}}\\\\<br \/>\n&#038; =\\sqrt[n]{\\dfrac{600}{25^{n+1}(25-1)}}\\\\<br \/>\n&#038; =\\sqrt[n]{\\dfrac{\\cancel{600}^{25}}{25^{n+1}\\cdot\\cancel{24}}}\\\\<br \/>\n&#038;=\\sqrt[n]{\\dfrac{25}{25^{n+1}}}\\\\<br \/>\n&#038;= \\sqrt[n]{\\dfrac{\\cancel{25}}{25^n\\cdot \\cancel{25}}}\\\\<br \/>\n&#038;=\\sqrt[n]{\\dfrac{1}{25^n}}\\\\<br \/>\n&#038; =\\dfrac{1}{25}.<br \/>\n\\end{align*}[\/tex]<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:10px\">\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 9\u00ba ano do E. F.) Simplifique a express\u00e3o [tex]\\sqrt[n]{\\dfrac{600}{25^{n+2}-5^{2n+2}}}[\/tex]. Solu\u00e7\u00e3o [tex] \\begin{align*}\\sqrt[n]{\\dfrac{600}{25^{n+2}-5^{2n+2}}}&#038; =\\sqrt[n]{\\dfrac{600}{25^{n+2}-(5^2)^{n+1}}} \\\\ &#038;=\\sqrt[n]{\\dfrac{600}{25^{n+2}-25^{n+1}}}\\\\ &#038; =\\sqrt[n]{\\dfrac{600}{25^{n+1}(25-1)}}\\\\ &#038; =\\sqrt[n]{\\dfrac{\\cancel{600}^{25}}{25^{n+1}\\cdot\\cancel{24}}}\\\\ &#038;=\\sqrt[n]{\\dfrac{25}{25^{n+1}}}\\\\ &#038;= \\sqrt[n]{\\dfrac{\\cancel{25}}{25^n\\cdot \\cancel{25}}}\\\\ &#038;=\\sqrt[n]{\\dfrac{1}{25^n}}\\\\ &#038; =\\dfrac{1}{25}. \\end{align*}[\/tex] Solu\u00e7\u00e3o elaborada pelos Moderadores do Blog.<\/p>\n","protected":false},"author":164,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-72774","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/72774","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/164"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=72774"}],"version-history":[{"count":31,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/72774\/revisions"}],"predecessor-version":[{"id":186422,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/72774\/revisions\/186422"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=72774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}