{"id":23017,"date":"2022-11-05T01:34:43","date_gmt":"2022-11-05T01:34:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23017"},"modified":"2022-11-08T21:58:31","modified_gmt":"2022-11-08T21:58:31","slug":"associa-a-cada-expressao-o-resultado-correto","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23017","title":{"rendered":"Associa a cada express\u00e3o o resultado correto"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23017' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23017' class='GTTabs_curr'><a  id=\"23017_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23017' ><a  id=\"23017_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_23017'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Associa a cada express\u00e3o o resultado correto:<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"text-align: right;\">\\(\\sqrt 2 + \\sqrt 2 \\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0A\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0I\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(\\sqrt 2 \\times \\sqrt 2 \\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0B\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0II\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(\\sqrt 2 \\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(\\frac{{10\\sqrt 2 }}{5}\\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0C\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0III\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(2\\sqrt 2 \\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(\\sqrt 2 \\left( {\\sqrt 2 &#8211; 1} \\right)\\left( {\\sqrt 2 + 1} \\right)\\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0D\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0IV\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(4\\sqrt 2 \\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(5\\sqrt 2 &#8211; 3\\sqrt 2 \\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0E\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td style=\"text-align: left;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\({\\left( {\\sqrt 2 + 1} \\right)^2} &#8211; {\\left( {\\sqrt 2 &#8211; 1} \\right)^2}\\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0F\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td style=\"text-align: left;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\({\\left( {\\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}} \\right)^2}\\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0G\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td style=\"text-align: left;\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23017' onClick='GTTabs_show(1,23017)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23017'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Comecemos por determinar, por escrito, o valor de cada uma das express\u00f5es, ainda que para algumas delas se possa determinar facilmente utilizando c\u00e1lculo mental.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"text-align: right;\">\\(\\sqrt 2 + \\sqrt 2 = 2\\sqrt 2 \\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0A\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0I\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(\\sqrt 2 \\times \\sqrt 2 = {\\left( {\\sqrt 2 } \\right)^2} = 2\\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0B\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0II\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(\\sqrt 2 \\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(\\frac{{10\\sqrt 2 }}{5} = 2\\sqrt 2 \\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0C\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0III\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(2\\sqrt 2 \\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(\\sqrt 2 \\left( {\\sqrt 2 &#8211; 1} \\right)\\left( {\\sqrt 2 + 1} \\right) = \\sqrt 2 \\left( {{{\\left( {\\sqrt 2 } \\right)}^2} + \\sqrt 2 &#8211; \\sqrt 2 &#8211; 1} \\right) = \\sqrt 2 \\times 1 = \\sqrt 2 \\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0D\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0IV\u00a0<\/span><\/td>\n<td style=\"text-align: left;\">\\(4\\sqrt 2 \\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(5\\sqrt 2 &#8211; 3\\sqrt 2 = 2\\sqrt 2 \\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0E\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td style=\"text-align: left;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\(\\begin{array}{*{20}{l}}{{{\\left( {\\sqrt 2 + 1} \\right)}^2} &#8211; {{\\left( {\\sqrt 2 &#8211; 1} \\right)}^2}}&amp; = &amp;{\\left( {\\sqrt 2 + 1} \\right)\\left( {\\sqrt 2 + 1} \\right) &#8211; \\left( {\\sqrt 2 &#8211; 1} \\right)\\left( {\\sqrt 2 &#8211; 1} \\right)}\\\\{}&amp; = &amp;{\\left( {{{\\left( {\\sqrt 2 } \\right)}^2} + \\sqrt 2 + \\sqrt 2 + 1} \\right) &#8211; \\left( {{{\\left( {\\sqrt 2 } \\right)}^2} &#8211; \\sqrt 2 &#8211; \\sqrt 2 + 1} \\right)}\\\\{}&amp; = &amp;{2 + 2\\sqrt 2 + 1 &#8211; 2 + 2\\sqrt 2 &#8211; 1}\\\\{}&amp; = &amp;{4\\sqrt 2 }\\end{array}\\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0F\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td style=\"text-align: left;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\">\\({\\left( {\\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}} \\right)^2} = {\\left( {\\sqrt 2 } \\right)^2} = 2\\)<\/td>\n<td><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0G\u00a0<\/span><\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td style=\"text-align: left;\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 69px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"width: 25%; height: 23px;\" colspan=\"4\">Associa\u00e7\u00e3o dos resultados<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 25%; height: 23px;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0I\u00a0<\/span><span style=\"color: #000000;\">\u00a0 \\(2\\)<\/span><\/td>\n<td style=\"width: 25%; height: 23px;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0II\u00a0<\/span><span style=\"color: #000000;\">\u00a0 \\(\\sqrt 2 \\)<\/span><\/td>\n<td style=\"width: 25%; height: 23px;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0III\u00a0<\/span><span style=\"color: #000000;\">\u00a0 \\(2\\sqrt 2 \\)<\/span><\/td>\n<td style=\"width: 25%; height: 23px;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0IV\u00a0<\/span><span style=\"color: #000000;\">\u00a0 \\(4\\sqrt 2 \\)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"color: #000000;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0B\u00a0<\/span> \u00a0<span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0G\u00a0<\/span><\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0D\u00a0<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0A <\/span>\u00a0 <span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0C <\/span>\u00a0 <span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0E\u00a0<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"background-color: #8a1e1e; color: #ffffff;\">\u00a0F\u00a0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23017' onClick='GTTabs_show(0,23017)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Associa a cada express\u00e3o o resultado correto: \\(\\sqrt 2 + \\sqrt 2 \\) \u00a0A\u00a0 \u00a0 \u00a0I\u00a0 \\(2\\) \\(\\sqrt 2 \\times \\sqrt 2 \\) \u00a0B\u00a0 \u00a0 \u00a0II\u00a0 \\(\\sqrt 2 \\) \\(\\frac{{10\\sqrt 2&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19176,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,450],"series":[],"class_list":["post-23017","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-operacoes-com-numeros-reais"],"views":280,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat67.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23017","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=23017"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23017\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19176"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23017"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}