{"id":22982,"date":"2022-11-04T21:35:38","date_gmt":"2022-11-04T21:35:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22982"},"modified":"2022-11-08T10:24:24","modified_gmt":"2022-11-08T10:24:24","slug":"calcula-o-valor-das-expressoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22982","title":{"rendered":"Calcula o valor das express\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22982' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22982' class='GTTabs_curr'><a  id=\"22982_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22982' ><a  id=\"22982_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_22982'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcula o valor das express\u00f5es, tendo em aten\u00e7\u00e3o as propriedades das opera\u00e7\u00f5es.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\(2\\sqrt 3 + 4\\sqrt 3 &#8211; 5\\sqrt 3 \\)<\/li>\n<li>\\({\\left( {\\sqrt 2 + 2} \\right)^2}\\)<\/li>\n<li>\\(\\frac{1}{3}\\pi &#8211; \\pi + 3\\pi \\)<\/li>\n<li>\\(\\left( {5 &#8211; \\sqrt 5 } \\right)\\left( {5 + \\sqrt 5 } \\right)\\)<\/li>\n<li>\\({\\left( {\\sqrt 7 &#8211; 1} \\right)^2}\\)<\/li>\n<li>\\(\\left( {2 + \\sqrt 3 } \\right)\\left( {7 &#8211; \\sqrt 3 } \\right)\\)<\/li>\n<li>\\(\\sqrt 5 &#8211; \\sqrt 6 + 2\\sqrt 5 &#8211; 2\\sqrt 6 \\)<\/li>\n<li>\\(\\sqrt {\\frac{9}{{25}}} &#8211; \\frac{4}{5} + \\sqrt 2 \\)<\/li>\n<li>\\(\\left( {\\sqrt 2 + 1} \\right)\\left( {\\sqrt 2 &#8211; 1} \\right)\\)<\/li>\n<li>\\(\\left( {\\sqrt {10} &#8211; \\sqrt {11} } \\right)\\left( {\\sqrt {10} &#8211; \\sqrt {11} } \\right)\\)<\/li>\n<li>\\({\\left( {2\\sqrt 3 } \\right)^2}\\)<\/li>\n<li>\\({\\left( {3\\sqrt 2 } \\right)^2}\\)<\/li>\n<li>\\({\\left( {3\\sqrt 5 } \\right)^2}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22982' onClick='GTTabs_show(1,22982)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22982'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Tendo em aten\u00e7\u00e3o as propriedades das opera\u00e7\u00f5es, apresenta-se o c\u00e1lculo das express\u00f5es dadas:<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 658px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 5.98958%;\">Al\u00ednea<\/td>\n<td style=\"height: 23px; width: 93.8802%;\">C\u00e1lculo da express\u00e3o<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">a)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\(2\\sqrt 3 + 4\\sqrt 3 &#8211; 5\\sqrt 3 = \\left( {2 + 4 &#8211; 5} \\right) \\times \\sqrt 3 = \\sqrt 3 \\)<\/td>\n<\/tr>\n<tr style=\"height: 65px;\">\n<td style=\"height: 65px; width: 5.98958%;\">b)<\/td>\n<td style=\"height: 65px; width: 93.8802%; text-align: left;\">\\({\\left( {\\sqrt 2 + 2} \\right)^2} = \\left( {\\sqrt 2 + 2} \\right)\\left( {\\sqrt 2 + 2} \\right) = {\\left( {\\sqrt 2 } \\right)^2} + 2\\sqrt 2 + 2\\sqrt 2 + 4 = 2 + 4\\sqrt 2 + 4 = 6 + 4\\sqrt 2 \\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">c)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\(\\frac{1}{3}\\pi &#8211; \\pi + 3\\pi = \\left( {\\frac{1}{3} &#8211; 1 + 3} \\right)\\pi = \\frac{7}{3}\\pi \\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">d)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\(\\left( {5 &#8211; \\sqrt 5 } \\right)\\left( {5 + \\sqrt 5 } \\right) = 25 + 5\\sqrt 5 &#8211; 5\\sqrt 5 &#8211; {\\left( {\\sqrt 5 } \\right)^2} = 25 &#8211; 5 = 20\\)<\/td>\n<\/tr>\n<tr style=\"height: 65px;\">\n<td style=\"height: 65px; width: 5.98958%;\">e)<\/td>\n<td style=\"height: 65px; width: 93.8802%; text-align: left;\">\\({\\left( {\\sqrt 7 &#8211; 1} \\right)^2} = \\left( {\\sqrt 7 &#8211; 1} \\right)\\left( {\\sqrt 7 &#8211; 1} \\right) = {\\left( {\\sqrt 7 } \\right)^2} &#8211; \\sqrt 7 &#8211; \\sqrt 7 + 1 = 7 &#8211; 2\\sqrt 7 + 1 = 8 &#8211; 2\\sqrt 7 \\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">f)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\(\\left( {2 + \\sqrt 3 } \\right)\\left( {7 &#8211; \\sqrt 3 } \\right) = 14 &#8211; 2\\sqrt 3 + 7\\sqrt 3 &#8211; {\\left( {\\sqrt 3 } \\right)^2} = 14 + 5\\sqrt 3 &#8211; 3 = 11 + 5\\sqrt 3 \\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">g)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\(\\sqrt 5 &#8211; \\sqrt 6 + 2\\sqrt 5 &#8211; 2\\sqrt 6 = \\left( {\\sqrt 5 + 2\\sqrt 5 } \\right) + \\left( { &#8211; \\sqrt 6 &#8211; 2\\sqrt 6 } \\right) = 3\\sqrt 5 &#8211; 3\\sqrt 6 \\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">h)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\(\\sqrt {\\frac{9}{{25}}} &#8211; \\frac{4}{5} + \\sqrt 2 = \\frac{3}{5} &#8211; \\frac{4}{5} + \\sqrt 2 = &#8211; \\frac{1}{5} + \\sqrt 2 \\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">i)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\(\\left( {\\sqrt 2 + 1} \\right)\\left( {\\sqrt 2 &#8211; 1} \\right) = {\\left( {\\sqrt 2 } \\right)^2} &#8211; \\sqrt 2 + \\sqrt 2 &#8211; 1 = 2 &#8211; 1 = 1\\)<\/td>\n<\/tr>\n<tr style=\"height: 65px;\">\n<td style=\"height: 65px; width: 5.98958%;\">j)<\/td>\n<td style=\"height: 65px; width: 93.8802%; text-align: left;\">\\(\\left( {\\sqrt {10} &#8211; \\sqrt {11} } \\right)\\left( {\\sqrt {10} + \\sqrt {11} } \\right) = {\\left( {\\sqrt {10} } \\right)^2} + \\sqrt {10} \\times \\sqrt {11} &#8211; \\sqrt {10} \\times \\sqrt {11} &#8211; {\\left( {\\sqrt {11} } \\right)^2} = 10 &#8211; 11 = &#8211; 1\\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">k)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\({\\left( {2\\sqrt 3 } \\right)^2} = {2^2} \\times {\\left( {\\sqrt 3 } \\right)^2} = 4 \\times 3 = 12\\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">l)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\({\\left( {3\\sqrt 2 } \\right)^2} = 3\\sqrt 2 \\times 3\\sqrt 2 = \\left( {3 \\times 3} \\right) \\times \\left( {\\sqrt 2 \\times \\sqrt 2 } \\right) = 9 \\times 2 = 18\\)<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 5.98958%;\">m)<\/td>\n<td style=\"height: 44px; width: 93.8802%; text-align: left;\">\\({\\left( {3\\sqrt 5 } \\right)^2} = {3^2} \\times {\\left( {\\sqrt 5 } \\right)^2} = 9 \\times 5 = 45\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22982' onClick='GTTabs_show(0,22982)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula o valor das express\u00f5es, tendo em aten\u00e7\u00e3o as propriedades das opera\u00e7\u00f5es. \\(2\\sqrt 3 + 4\\sqrt 3 &#8211; 5\\sqrt 3 \\) \\({\\left( {\\sqrt 2 + 2} \\right)^2}\\) \\(\\frac{1}{3}\\pi &#8211; \\pi +&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19172,"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-22982","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":313,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat63.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22982","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=22982"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22982\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19172"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22982"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22982"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22982"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}