{"id":170432,"date":"2024-11-19T20:08:24","date_gmt":"2024-11-19T20:08:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170432"},"modified":"2024-11-19T20:08:26","modified_gmt":"2024-11-19T20:08:26","slug":"which-statements-are-true","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/which-statements-are-true\/","title":{"rendered":"Which statements are true"},"content":{"rendered":"\n<p>Which statements are true? Select all that apply.<br>81 is a perfect square.<br>75 is a perfect cube.<br>729 is a perfect cube.<br>32 is neither a perfect square nor a perfect cube.<br>81 is both a perfect square and a perfect cube.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answers:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>81 is a perfect square.<\/strong> \u2705<\/li>\n\n\n\n<li><strong>729 is a perfect cube.<\/strong> \u2705<\/li>\n\n\n\n<li><strong>32 is neither a perfect square nor a perfect cube.<\/strong> \u2705<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>1. 81 is a perfect square.<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A perfect square is a number that can be expressed as the square of an integer.<br>[<br>9 \\times 9 = 81<br>]<br>Since 81 is ( 9^2 ), it is a perfect square.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>2. 75 is a perfect cube.<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A perfect cube is a number that can be expressed as the cube of an integer.<br>Testing integers:<br>[<br>4^3 = 64, \\quad 5^3 = 125<br>]<br>Since 75 is not between ( 4^3 ) and ( 5^3 ), it is not a perfect cube.<br><strong>This statement is false.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>3. 729 is a perfect cube.<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( 729 = 9 \\times 9 \\times 9 = 9^3 ).<br>Since it can be expressed as the cube of an integer (( 9 )), it is a perfect cube.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>4. 32 is neither a perfect square nor a perfect cube.<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Testing for perfect squares:<br>[<br>5^2 = 25, \\quad 6^2 = 36<br>]<br>Since ( 32 ) is not the square of any integer, it is not a perfect square.<\/li>\n\n\n\n<li>Testing for perfect cubes:<br>[<br>3^3 = 27, \\quad 4^3 = 64<br>]<br>Similarly, ( 32 ) is not the cube of any integer, so it is not a perfect cube.<br><strong>This statement is true.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>5. 81 is both a perfect square and a perfect cube.<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( 81 = 9^2 ), so it is a perfect square.<\/li>\n\n\n\n<li>Testing for cubes:<br>[<br>4^3 = 64, \\quad 5^3 = 125<br>]<br>( 81 ) is not a perfect cube.<br><strong>This statement is false.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>True Statements:<\/strong><\/li>\n\n\n\n<li>81 is a perfect square.<\/li>\n\n\n\n<li>729 is a perfect cube.<\/li>\n\n\n\n<li>32 is neither a perfect square nor a perfect cube.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Which statements are true? Select all that apply.81 is a perfect square.75 is a perfect cube.729 is a perfect cube.32 is neither a perfect square nor a perfect cube.81 is both a perfect square and a perfect cube. The Correct Answer and Explanation is : Correct Answers: Explanation: 1. 81 is a perfect square. 2. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-170432","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170432","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=170432"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170432\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}