{"id":22974,"date":"2022-11-04T01:21:52","date_gmt":"2022-11-04T01:21:52","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22974"},"modified":"2022-11-07T01:09:15","modified_gmt":"2022-11-07T01:09:15","slug":"calcula-o-valor-das-seguintes-expressoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22974","title":{"rendered":"Calcula o valor das seguintes express\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22974' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22974' class='GTTabs_curr'><a  id=\"22974_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22974' ><a  id=\"22974_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_22974'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sabendo que as propriedades das opera\u00e7\u00f5es e as regras de c\u00e1lculo em \\(\\mathbb{Q}\\) se mant\u00eam v\u00e1lidas para os n\u00fameros reais, calcula o valor das seguintes express\u00f5es num\u00e9ricas e identifica as propriedades usadas.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\(3\\pi + 5\\pi \\)<\/li>\n<li>\\(4\\sqrt 2 &#8211; 7\\sqrt 2 \\)<\/li>\n<li>\\(\\sqrt 3 \\left( {1 + \\frac{1}{{\\sqrt 3 }}} \\right)\\)<\/li>\n<li>\\({\\left( {1 + \\sqrt 2 } \\right)^2}\\)<\/li>\n<li>\\(3\\pi + 2\\sqrt 5 &#8211; 3\\sqrt 5 \\)<\/li>\n<li>\\({\\left( {4\\sqrt 3 } \\right)^2}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22974' onClick='GTTabs_show(1,22974)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22974'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 224px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px;\"><strong>Al\u00ednea<\/strong><\/td>\n<td style=\"height: 23px;\"><strong>C\u00e1lculo<\/strong><\/td>\n<td style=\"height: 23px;\"><strong>Propriedades<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px;\">a)<\/td>\n<td style=\"text-align: left; height: 23px;\">\\(3\\pi + 5\\pi = \\left( {3 + 5} \\right) \\times \\pi = 8\\pi \\)<\/td>\n<td style=\"height: 23px;\">I<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px;\">b)<\/td>\n<td style=\"text-align: left; height: 23px;\">\\(4\\sqrt 2 &#8211; 7\\sqrt 2 = \\left( {4 &#8211; 7} \\right) \\times \\sqrt 2 = &#8211; 3\\sqrt 2 \\)<\/td>\n<td style=\"height: 23px;\">II<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px;\">c)<\/td>\n<td style=\"text-align: left; height: 44px;\">\\(\\sqrt 3 \\left( {1 + \\frac{1}{{\\sqrt 3 }}} \\right) = \\sqrt 3 \\times 1 + \\sqrt 3 \\times \\frac{1}{{\\sqrt 3 }} = \\sqrt 3 + 1\\)<\/td>\n<td style=\"height: 44px;\">I e III<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px;\">d)<\/td>\n<td style=\"text-align: left; height: 44px;\">\\({\\left( {1 + \\sqrt 2 } \\right)^2} = \\left( {1 + \\sqrt 2 } \\right)\\left( {1 + \\sqrt 2 } \\right) = 1 + \\sqrt 2 + \\sqrt 2 + {\\left( {\\sqrt 2 } \\right)^2} = 1 + 2\\sqrt 2 + 2 = 3 + 2\\sqrt 2 \\)<\/td>\n<td style=\"height: 44px;\">I, III, IV e V<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px;\">e)<\/td>\n<td style=\"text-align: left; height: 23px;\">\\(3\\pi + 2\\sqrt 5 &#8211; 3\\sqrt 5 = 3\\pi + \\left( {2 &#8211; 3} \\right) \\times \\sqrt 5 = 3\\pi &#8211; \\sqrt 5 \\)<\/td>\n<td style=\"height: 23px;\">IV e II<\/td>\n<\/tr>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px;\">f)<\/td>\n<td style=\"text-align: left; height: 44px;\">\\({\\left( {4\\sqrt 3 } \\right)^2} = 4\\sqrt 3 \\times 4\\sqrt 3 = \\left( {4 \\times 4} \\right) + \\left( {\\sqrt 3 \\times \\sqrt 3 } \\right) = {4^2} \\times {\\left( {\\sqrt 3 } \\right)^2} = 16 \\times 3 = 48\\)<\/td>\n<td style=\"height: 44px;\">VI e VII<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 115px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"width: 4.29688%; height: 23px;\">I<\/td>\n<td style=\"width: 95.5729%; height: 23px; text-align: left;\">Propriedade distributiva da multiplica\u00e7\u00e3o em rela\u00e7\u00e3o \u00e0 adi\u00e7\u00e3o<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 4.29688%; height: 23px;\">II<\/td>\n<td style=\"width: 95.5729%; height: 23px; text-align: left;\">Propriedade distributiva da multiplica\u00e7\u00e3o em rela\u00e7\u00e3o \u00e0 subtra\u00e7\u00e3o<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 4.29688%; height: 23px;\">III<\/td>\n<td style=\"width: 95.5729%; height: 23px; text-align: left;\">Propriedade da exist\u00eancia de elemento neutro da multiplica\u00e7\u00e3o<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 4.29688%; height: 23px;\">IV<\/td>\n<td style=\"width: 95.5729%; height: 23px; text-align: left;\">Propriedade associativa da adi\u00e7\u00e3o<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 4.29688%; height: 23px;\">V<\/td>\n<td style=\"width: 95.5729%; height: 23px; text-align: left;\">Propriedade comutativa da adi\u00e7\u00e3o<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 4.29688%;\">VI<\/td>\n<td style=\"width: 95.5729%; text-align: left;\">Propriedade associativa da multiplica\u00e7\u00e3o<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 4.29688%;\">VII<\/td>\n<td style=\"width: 95.5729%; text-align: left;\">Propriedade comutativa da multiplica\u00e7\u00e3o<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n\n\n\n<p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22974' onClick='GTTabs_show(0,22974)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabendo que as propriedades das opera\u00e7\u00f5es e as regras de c\u00e1lculo em \\(\\mathbb{Q}\\) se mant\u00eam v\u00e1lidas para os n\u00fameros reais, calcula o valor das seguintes express\u00f5es num\u00e9ricas e identifica as propriedades&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19189,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,262,266,681],"series":[],"class_list":["post-22974","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-racionais","tag-numeros-reais","tag-propriedades-das-operacoes"],"views":270,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22974","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=22974"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22974\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22974"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}