{"id":12827,"date":"2017-10-29T11:55:59","date_gmt":"2017-10-29T11:55:59","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12827"},"modified":"2022-01-15T23:30:04","modified_gmt":"2022-01-15T23:30:04","slug":"aproxima-sqrt35-as-decimas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12827","title":{"rendered":"Aproxima \\(\\sqrt[3]{5}\\) \u00e0s d\u00e9cimas"},"content":{"rendered":"<p><ul id='GTTabs_ul_12827' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12827' class='GTTabs_curr'><a  id=\"12827_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12827' ><a  id=\"12827_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_12827'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Aproxima \\(\\sqrt[3]{5}\\) \u00e0s d\u00e9cimas.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12827' onClick='GTTabs_show(1,12827)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12827'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Aproxima \\(\\sqrt[3]{5}\\) \u00e0s d\u00e9cimas.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Calculo4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12832\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12832\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Calculo4.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Calculo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Calculo4.png\" class=\"alignright size-full wp-image-12832\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Calculo4.png\" alt=\"\" width=\"198\" height=\"134\" \/><\/a>Utilizando a calculadora, podemos indicar\u00a0\\(\\sqrt[3]{5} \\approx 1,7\\), com aproxima\u00e7\u00e3o \u00e0s d\u00e9cimas.<\/p>\n<\/p>\n<p><strong>Em alternativa<\/strong>, podemos utilizar o m\u00e9todo dos cubos perfeitos:<\/p>\n<p>Ora, tem-se\u00a0\\(x = \\sqrt[3]{5}\\) e\u00a0\\(r = 0,1 = \\frac{1}{{10}}\\). Logo,\u00a0\\(n = 10\\).<\/p>\n<p>Assim, vem sucessivamente:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{4913 &lt; {{10}^3} \\times 5 &lt; 5832}\\\\{{{\\left( {\\frac{{17}}{{10}}} \\right)}^3} &lt; 5 &lt; {{\\left( {\\frac{{18}}{{10}}} \\right)}^3}}\\\\{1,7 &lt; \\sqrt[3]{5} &lt; 1,8}\\end{array}\\]<\/p>\n<p>Como\u00a0\\(\\left| {{{1,7}^3} &#8211; 5} \\right| = 0,087\\) e\u00a0\\(\\left| {{{1,8}^3} &#8211; 5} \\right| = 0,832\\), ent\u00e3o\u00a0\\(\\sqrt[3]{5} \\approx 1,7\\), com aproxima\u00e7\u00e3o \u00e0s d\u00e9cimas.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12827' onClick='GTTabs_show(0,12827)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Aproxima \\(\\sqrt[3]{5}\\) \u00e0s d\u00e9cimas. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20309,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[443,442],"series":[],"class_list":["post-12827","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-enquadramento","tag-valor-aproximado"],"views":2919,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag024-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12827","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=12827"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12827\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20309"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12827"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12827"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12827"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}