{"id":22901,"date":"2022-11-02T19:08:04","date_gmt":"2022-11-02T19:08:04","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22901"},"modified":"2022-11-02T19:49:26","modified_gmt":"2022-11-02T19:49:26","slug":"copia-e-completa-8","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22901","title":{"rendered":"Copia e completa"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22901' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22901' class='GTTabs_curr'><a  id=\"22901_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22901' ><a  id=\"22901_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_22901'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Copia e completa com os s\u00edmbolos \\( \\in \\) ou \\( \\notin \\).<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 67px;\">\n<tbody>\n<tr style=\"height: 44px;\">\n<td style=\"width: 25%; height: 44px;\">\\(\\sqrt {16} \\ldots \\mathbb{N}\\)<\/td>\n<td style=\"width: 25%; height: 44px;\">\\( &#8211; \\frac{{17}}{3} \\ldots {\\mathbb{Q}^ &#8211; }\\)<\/td>\n<td style=\"width: 25%; height: 44px;\">\\(0 \\ldots {\\mathbb{Z}^ &#8211; }\\)<\/td>\n<td style=\"width: 25%; height: 44px;\">\\( &#8211; \\sqrt 3 \\ldots \\mathbb{R}_0^ &#8211; \\)<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 25%; height: 23px;\">\\(\\sqrt {25} \\ldots \\mathbb{N}\\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(\\sqrt[3]{{\\frac{{729}}{{27}}}} \\ldots \\mathbb{Q}\\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\(0 \\ldots {\\mathbb{R}^ + }\\)<\/td>\n<td style=\"width: 25%; height: 23px;\">\\( &#8211; \\sqrt {\\frac{{36}}{9}} \\ldots \\mathbb{Z}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22901' onClick='GTTabs_show(1,22901)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22901'>\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<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td><strong>Al\u00ednea<\/strong><\/td>\n<td><strong>Completa\u00e7\u00e3o<\/strong><\/td>\n<td><strong>Justifica\u00e7\u00e3o<\/strong><\/td>\n<\/tr>\n<tr>\n<td>a)<\/td>\n<td>\\(\\sqrt {16} \\in \\mathbb{N}\\)<\/td>\n<td>\\(\\sqrt {16} = 4\\) \u00e9 um n\u00famero natural.<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td>\\( &#8211; \\frac{{17}}{3} \\in {\\mathbb{Q}^ &#8211; }\\)<\/td>\n<td>\\( &#8211; \\frac{{17}}{3}\\) \u00e9 um n\u00famero racional e negativo.<\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td>\\(0 \\notin {\\mathbb{Z}^ &#8211; }\\)<\/td>\n<td>\\(0\\) \u00e9 um n\u00famero inteiro, mas n\u00e3o negativo (\u00e9 nulo).<\/td>\n<\/tr>\n<tr>\n<td>d)<\/td>\n<td>\\( &#8211; \\sqrt 3 \\in \\mathbb{R}_0^ &#8211; \\)<\/td>\n<td>\\( &#8211; \\sqrt 3 \\) \u00e9 um n\u00famero irracional negativo e, consequentemente, \u00e9 real negativo.<\/td>\n<\/tr>\n<tr>\n<td>e)<\/td>\n<td>\\(\\sqrt {25} \\in \\mathbb{N}\\)<\/td>\n<td>\\(\\sqrt {25} = 5\\) \u00e9 um n\u00famero natural<\/td>\n<\/tr>\n<tr>\n<td>f)<\/td>\n<td>\\(\\sqrt[3]{{\\frac{{729}}{{27}}}} \\in \\mathbb{Q}\\)<\/td>\n<td>\\(\\sqrt[3]{{\\frac{{729}}{{27}}}} = \\sqrt[3]{{\\frac{{{9^3}}}{{{3^3}}}}} = \\frac{9}{3} = 3\\) \u00e9 um n\u00famero inteiro. Logo, tamb\u00e9m \u00e9 racional.<\/td>\n<\/tr>\n<tr>\n<td>g)<\/td>\n<td>\\(0 \\notin {\\mathbb{R}^ + }\\)<\/td>\n<td>\\(0\\) \u00e9 um n\u00famero real, mas \u00e9 nulo.<\/td>\n<\/tr>\n<tr>\n<td>h)<\/td>\n<td>\\( &#8211; \\sqrt {\\frac{{36}}{9}} \\in \\mathbb{Z}\\)<\/td>\n<td>\\( &#8211; \\sqrt {\\frac{{36}}{9}} = &#8211; \\sqrt 4 = &#8211; 2\\) \u00e9 um n\u00famero inteiro.<\/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_22901' onClick='GTTabs_show(0,22901)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Copia e completa com os s\u00edmbolos \\( \\in \\) ou \\( \\notin \\). \\(\\sqrt {16} \\ldots \\mathbb{N}\\) \\( &#8211; \\frac{{17}}{3} \\ldots {\\mathbb{Q}^ &#8211; }\\) \\(0 \\ldots {\\mathbb{Z}^ &#8211; }\\) \\( &#8211;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19171,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,319,259,680,262,266],"series":[],"class_list":["post-22901","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-inteiros-2","tag-numeros-irracionais","tag-numeros-naturais","tag-numeros-racionais","tag-numeros-reais"],"views":205,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat62.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22901","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=22901"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22901\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22901"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}