{"id":22869,"date":"2022-11-02T14:27:05","date_gmt":"2022-11-02T14:27:05","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22869"},"modified":"2022-11-02T16:17:49","modified_gmt":"2022-11-02T16:17:49","slug":"quais-sao-os-numeros-irracionais","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22869","title":{"rendered":"Quais s\u00e3o os n\u00fameros irracionais?"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22869' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22869' class='GTTabs_curr'><a  id=\"22869_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22869' ><a  id=\"22869_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_22869'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Indica, de entre os seguintes n\u00fameros, quais s\u00e3o irracionais. Justifica a tua op\u00e7\u00e3o.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 90px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"width: 25%; height: 23px;\">\\(\\pi \\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(1,\\left( {02} \\right)\\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(\\sqrt 3 \\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(\\frac{{15}}{{25}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"width: 25%; height: 44px;\">\\(\\frac{{\\sqrt 7 }}{{\\sqrt 7 }}\\)<\/td>\n<td style=\"width: 25%; height: 44px;\">\\(\\frac{{51}}{{11}}\\)<\/td>\n<td style=\"width: 25%; height: 44px;\">\\(\\sqrt {64} \\)<\/td>\n<td style=\"width: 25%; height: 44px;\">\\(\\frac{1}{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 25%; height: 23px;\">\\(\\sqrt[3]{{ &#8211; 27}}\\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(\\sqrt 8 \\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(\\sqrt[3]{8}\\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(\\sqrt {\\frac{4}{9}} \\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22869' onClick='GTTabs_show(1,22869)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22869'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Recorda-se que os n\u00fameros racionais podem ser representados na forma de fra\u00e7\u00e3o, quer na forma de d\u00edzima finita ou infinita peri\u00f3dica.<\/p>\n<\/blockquote>\n<p>Apenas s\u00e3o irracionais: (A) \\(\\pi \\); (C) \\(\\sqrt 3 \\) e (J) \\(\\sqrt 8 \\).<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td><strong>Al\u00ednea<\/strong><\/td>\n<td><strong>N\u00famero<\/strong><\/td>\n<td><strong>N\u00famero racional<\/strong><\/td>\n<td><strong>N\u00famero irracional<\/strong><\/td>\n<td><strong>Justifica\u00e7\u00e3o<\/strong><\/td>\n<\/tr>\n<tr>\n<td>(A)<\/td>\n<td>\\(\\pi \\)<\/td>\n<td>\u00a0<\/td>\n<td>X<\/td>\n<td>N\u00famero representado por um d\u00edzima infinita n\u00e3o peri\u00f3dica<\/td>\n<\/tr>\n<tr>\n<td>(B)<\/td>\n<td>\\(1,\\left( {02} \\right)\\)<\/td>\n<td>X<\/td>\n<td>\u00a0<\/td>\n<td>N\u00famero representado por uma d\u00edzima infinita peri\u00f3dica<\/td>\n<\/tr>\n<tr>\n<td>(C)<\/td>\n<td>\\(\\sqrt 3 \\)<\/td>\n<td>\u00a0<\/td>\n<td>X<\/td>\n<td>O n\u00famero \\(3\\) n\u00e3o \u00e9 um quadrado perfeito<\/td>\n<\/tr>\n<tr>\n<td>(D)<\/td>\n<td>\u00a0\\(\\frac{{15}}{{25}}\\)<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>N\u00famero que pode ser representado por uma d\u00edzima finita: \\(\\frac{{15}}{{25}} = \\frac{3}{5} = 0,6\\)<\/td>\n<\/tr>\n<tr>\n<td>(E)<\/td>\n<td>\\(\\frac{{\\sqrt 7 }}{{\\sqrt 7 }}\\)<\/td>\n<td>X<\/td>\n<td>\u00a0<\/td>\n<td>N\u00famero inteiro: \\(\\frac{{\\sqrt 7 }}{{\\sqrt 7 }} = 1\\)<\/td>\n<\/tr>\n<tr>\n<td>(F)<\/td>\n<td>\\(\\frac{{51}}{{11}}\\)<\/td>\n<td>X<\/td>\n<td>\u00a0<\/td>\n<td>N\u00famero que pode ser representado por uma d\u00edzima infinita peri\u00f3dica: \\(\\frac{{51}}{{11}} = 4,\\left( {63} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>(G)<\/td>\n<td>\\(\\sqrt {64} \\)<\/td>\n<td>X<\/td>\n<td>\u00a0<\/td>\n<td>O n\u00famero \\(64\\) \u00e9 um quadrado perfeito: \\(\\sqrt {64} = 8\\)<\/td>\n<\/tr>\n<tr>\n<td>(H)<\/td>\n<td>\\(\\frac{1}{3}\\)<\/td>\n<td>X<\/td>\n<td>\u00a0<\/td>\n<td>N\u00famero que pode ser representado por uma d\u00edzima infinita peri\u00f3dica: \\(\\frac{1}{3} = 0,\\left( 3 \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>(I)<\/td>\n<td>\\(\\sqrt[3]{{ &#8211; 27}}\\)<\/td>\n<td>X<\/td>\n<td>\u00a0<\/td>\n<td>O n\u00famero \\({27}\\) \u00e9 um cubo perfeito: \\(\\sqrt[3]{{ &#8211; 27}} = &#8211; 3\\)<\/td>\n<\/tr>\n<tr>\n<td>(J)<\/td>\n<td>\\(\\sqrt 8 \\)<\/td>\n<td>\u00a0<\/td>\n<td>X<\/td>\n<td>O n\u00famero \\(8\\) n\u00e3o \u00e9 um quadrado perfeito<\/td>\n<\/tr>\n<tr>\n<td>(K)<\/td>\n<td>\\(\\sqrt[3]{8}\\)<\/td>\n<td>X<\/td>\n<td>\u00a0<\/td>\n<td>O n\u00famero \\(8\\) \u00e9 um cubo perfeito: \\(\\sqrt[3]{8} = 2\\)<\/td>\n<\/tr>\n<tr>\n<td>(L)<\/td>\n<td>\\(\\sqrt {\\frac{4}{9}} \\)<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>Os n\u00fameros \\(4\\) e \\(9\\) s\u00e3o quadrados perfeitos: \\(\\sqrt {\\frac{4}{9}} = \\frac{2}{3} = 0,(6)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22869' onClick='GTTabs_show(0,22869)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Indica, de entre os seguintes n\u00fameros, quais s\u00e3o irracionais. Justifica a tua op\u00e7\u00e3o. \\(\\pi \\) \\(1,\\left( {02} \\right)\\) \\(\\sqrt 3 \\) \\(\\frac{{15}}{{25}}\\) \\(\\frac{{\\sqrt 7 }}{{\\sqrt 7 }}\\) \\(\\frac{{51}}{{11}}\\) \\(\\sqrt {64} \\)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,677,668,678,679],"series":[],"class_list":["post-22869","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-dizima-infinita-nao-periodica","tag-dizimas","tag-numero-irracional","tag-numero-racional"],"views":418,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=22869"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22869\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22869"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22869"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}