{"id":22993,"date":"2022-11-04T23:44:05","date_gmt":"2022-11-04T23:44:05","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22993"},"modified":"2022-11-08T21:57:36","modified_gmt":"2022-11-08T21:57:36","slug":"e-um-numero-irracional-ou-racional","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22993","title":{"rendered":"\u00c9 um n\u00famero irracional ou racional?"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22993' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22993' class='GTTabs_curr'><a  id=\"22993_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22993' ><a  id=\"22993_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_22993'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Averigua se \u00e9 um n\u00famero irracional ou um n\u00famero racional o valor de cada uma das seguintes express\u00f5es.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\(\\sqrt {12} &#8211; \\left( {1 + \\sqrt {12} } \\right)\\)<\/li>\n<li>\\( &#8211; \\sqrt {\\frac{1}{9}} &#8211; 1 + \\frac{4}{3} + \\sqrt {17} \\)<\/li>\n<li>\\(\\sqrt {\\frac{9}{4}} + \\left( {\\frac{1}{2} &#8211; \\sqrt 2 } \\right)\\left( {\\frac{1}{2} + \\sqrt 2 } \\right)\\)<\/li>\n<li>\\(10\\sqrt 5 &#8211; {\\left( {5 + \\sqrt 5 } \\right)^2}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22993' onClick='GTTabs_show(1,22993)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22993'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Calcula-se o valor de cada express\u00e3o e conclui-se se \u00e9 um n\u00famero irracional ou um n\u00famero racional:<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>Al\u00ednea<\/td>\n<td>C\u00e1lculo do valor da express\u00e3o\u00a0<\/td>\n<td>Valor irracional ou racional?<\/td>\n<\/tr>\n<tr>\n<td>a)<\/td>\n<td style=\"text-align: left;\">\\(\\sqrt {12} &#8211; \\left( {1 + \\sqrt {12} } \\right) = \\sqrt {12} &#8211; 1 &#8211; \\sqrt {12} = &#8211; 1\\)<\/td>\n<td>Racional<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td style=\"text-align: left;\">\\( &#8211; \\sqrt {\\frac{1}{9}} &#8211; 1 + \\frac{4}{3} + \\sqrt {17} = &#8211; \\frac{1}{3} &#8211; 1 + \\frac{4}{3} + \\sqrt {17} = 1 &#8211; 1 + \\sqrt {17} = \\sqrt {17} \\)<\/td>\n<td>Irracional<\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td style=\"text-align: left;\">\\[\\sqrt {\\frac{9}{4}} + \\left( {\\frac{1}{2} &#8211; \\sqrt 2 } \\right)\\left( {\\frac{1}{2} + \\sqrt 2 } \\right) = \\frac{3}{2} + {\\left( {\\frac{1}{2}} \\right)^2} + \\frac{{\\sqrt 2 }}{2} &#8211; \\frac{{\\sqrt 2 }}{2} &#8211; {\\left( {\\sqrt 2 } \\right)^2} = \\frac{6}{4} + \\frac{1}{4} &#8211; 2 = &#8211; \\frac{1}{4}\\]<\/td>\n<td>Racional<\/td>\n<\/tr>\n<tr>\n<td>d)<\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{10\\sqrt 5 &#8211; {{\\left( {5 + \\sqrt 5 } \\right)}^2}}&amp; = &amp;{10\\sqrt 5 &#8211; \\left( {5 + \\sqrt 5 } \\right)\\left( {5 + \\sqrt 5 } \\right)}\\\\{}&amp; = &amp;{10\\sqrt 5 &#8211; \\left( {{5^2} + 5\\sqrt 5 + 5\\sqrt 5 + {{\\left( {\\sqrt 5 } \\right)}^2}} \\right)}\\\\{}&amp; = &amp;{10\\sqrt 5 &#8211; \\left( {25 + 10\\sqrt 5 + 5} \\right)}\\\\{}&amp; = &amp;{10\\sqrt 5 &#8211; 25 &#8211; 10\\sqrt 5 &#8211; 5}\\\\{}&amp; = &amp;{ &#8211; 30}\\end{array}\\]<\/td>\n<td>Racional<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22993' onClick='GTTabs_show(0,22993)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Averigua se \u00e9 um n\u00famero irracional ou um n\u00famero racional o valor de cada uma das seguintes express\u00f5es. \\(\\sqrt {12} &#8211; \\left( {1 + \\sqrt {12} } \\right)\\) \\( &#8211; \\sqrt&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19174,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,259,262,266],"series":[],"class_list":["post-22993","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-numeros-irracionais","tag-numeros-racionais","tag-numeros-reais"],"views":322,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat65.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22993","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=22993"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22993\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19174"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22993"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22993"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22993"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}