{"id":12822,"date":"2017-10-29T11:40:19","date_gmt":"2017-10-29T11:40:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12822"},"modified":"2022-01-16T02:17:55","modified_gmt":"2022-01-16T02:17:55","slug":"enquadra-sqrt-7-por-numeros-racionais-com-erro-inferior-a-r-05","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12822","title":{"rendered":"Enquadra \\(\\sqrt 7 \\) por n\u00fameros racionais, com erro inferior a \\(r = 0,5\\)"},"content":{"rendered":"<p><ul id='GTTabs_ul_12822' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12822' class='GTTabs_curr'><a  id=\"12822_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12822' ><a  id=\"12822_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_12822'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Enquadra \\(\\sqrt 7 \\) por n\u00fameros racionais, com erro inferior a \\(r = 0,5\\).<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12822' onClick='GTTabs_show(1,12822)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12822'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Enquadra \\(\\sqrt 7 \\) por n\u00fameros racionais, com erro inferior a \\(r = 0,5\\).<\/p>\n<\/blockquote>\n<p>Tem-se\u00a0\\(x = \\sqrt 7 \\) e\u00a0\\(r = 0,5 = \\frac{1}{2}\\). Logo,\u00a0\\(n = 2\\).<\/p>\n<p>Assim, vem sucessivamente:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{25 &lt; {2^2} \\times 7 &lt; 36}\\\\{{{\\left( {\\frac{5}{2}} \\right)}^2} &lt; 7 &lt; {{\\left( {\\frac{6}{2}} \\right)}^2}}\\\\{2,5 &lt; \\sqrt 7 &lt; 3,0}\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12822' onClick='GTTabs_show(0,12822)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Enquadra \\(\\sqrt 7 \\) por n\u00fameros racionais, com erro inferior a \\(r = 0,5\\). Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20337,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[443,444,442],"series":[],"class_list":["post-12822","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-enquadramento","tag-erro","tag-valor-aproximado"],"views":4243,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag024-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12822","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=12822"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12822\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20337"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12822"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}