{"id":226334,"date":"2026-02-09T16:01:20","date_gmt":"2026-02-09T19:01:20","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=226334"},"modified":"2026-02-09T16:01:20","modified_gmt":"2026-02-09T19:01:20","slug":"problema-soma-de-radicais","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-soma-de-radicais\/","title":{"rendered":".Problema: Soma de Radicais"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\" style=\"line-height:25px;padding-bottom:15px\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 2\u00ba ano do E. M.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Qual o quadrado do n\u00famero [tex]\\sqrt{2+\\sqrt{3}}+\\sqrt{2-\\sqrt{3}}[\/tex]?<\/p>\n<\/div>\n<p style=\"margin:10px\">\n<p style=\"margin:40px\">\n<div class=\"g1n\" style=\"line-height:33px;\">\n<p class=\"tit\" style=\"line-height:20px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 30px;border: 0 none\"\/>\n<p>Seja [tex]a=\\sqrt{2+\\sqrt{3}}[\/tex] e [tex]b=\\sqrt{2-\\sqrt{3}}[\/tex]. Aplicando produtos not\u00e1veis, temos [tex](a+b)^2=a^2+2ab+b^2[\/tex]. Observe que:<\/p>\n<p>[tex]\\qquad a=\\sqrt{2+\\sqrt{3}}[\/tex] e [tex]a^2=(\\sqrt{2+\\sqrt{3}})^2=2+\\sqrt{3},[\/tex]<\/p>\n<p>[tex]\\qquad b=\\sqrt{2-\\sqrt{3}}[\/tex] e [tex]b^2=(\\sqrt{2-\\sqrt{3}})^2=2-\\sqrt{3},[\/tex]<\/p>\n<p>[tex]\\qquad 2ab=2\\cdot(\\sqrt{2+\\sqrt{3}})(\\sqrt{2-\\sqrt{3}})=2\\cdot(\\sqrt{2^2-(\\sqrt{3})^2})=2\\cdot(\\sqrt{4-3})=2.[\/tex]<\/p>\n<p>Portanto, <\/p>\n<p>[tex]\\qquad(a+b)^2=a^2+2ab+b^2=2+\\sqrt{3}+2+2-\\sqrt{3}=6.[\/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 pelo COM <strong> Villa-Lobos<\/strong>, com contribui\u00e7\u00f5es dos moderadores do Blog.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 2\u00ba ano do E. M.) Qual o quadrado do n\u00famero [tex]\\sqrt{2+\\sqrt{3}}+\\sqrt{2-\\sqrt{3}}[\/tex]? Solu\u00e7\u00e3o Seja [tex]a=\\sqrt{2+\\sqrt{3}}[\/tex] e [tex]b=\\sqrt{2-\\sqrt{3}}[\/tex]. Aplicando produtos not\u00e1veis, temos [tex](a+b)^2=a^2+2ab+b^2[\/tex]. Observe que: [tex]\\qquad a=\\sqrt{2+\\sqrt{3}}[\/tex] e [tex]a^2=(\\sqrt{2+\\sqrt{3}})^2=2+\\sqrt{3},[\/tex] [tex]\\qquad b=\\sqrt{2-\\sqrt{3}}[\/tex] e [tex]b^2=(\\sqrt{2-\\sqrt{3}})^2=2-\\sqrt{3},[\/tex] [tex]\\qquad 2ab=2\\cdot(\\sqrt{2+\\sqrt{3}})(\\sqrt{2-\\sqrt{3}})=2\\cdot(\\sqrt{2^2-(\\sqrt{3})^2})=2\\cdot(\\sqrt{4-3})=2.[\/tex] Portanto, [tex]\\qquad(a+b)^2=a^2+2ab+b^2=2+\\sqrt{3}+2+2-\\sqrt{3}=6.[\/tex] Solu\u00e7\u00e3o elaborada pelo COM Villa-Lobos, com contribui\u00e7\u00f5es dos moderadores do Blog. &nbsp;<\/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-226334","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/226334","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=226334"}],"version-history":[{"count":11,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/226334\/revisions"}],"predecessor-version":[{"id":229253,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/226334\/revisions\/229253"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=226334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}