{"id":280962,"date":"2025-08-05T09:43:32","date_gmt":"2025-08-05T09:43:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280962"},"modified":"2025-08-05T09:43:39","modified_gmt":"2025-08-05T09:43:39","slug":"look-at-this-equation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/05\/look-at-this-equation\/","title":{"rendered":"Look at this equation"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-512.png\" alt=\"\" class=\"wp-image-280963\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>q = 5<\/p>\n\n\n\n<p>The equation presented is&nbsp;q\u00b3 = 125. To solve for&nbsp;q, we need to understand what this equation represents. The term&nbsp;q\u00b3&nbsp;signifies&nbsp;q&nbsp;raised to the third power, which is the mathematical operation of multiplying&nbsp;q&nbsp;by itself three times (q \u00d7 q \u00d7 q). The problem asks us to find the specific value of&nbsp;q&nbsp;that makes this statement true. This process involves finding the cube root of 125.<\/p>\n\n\n\n<p>The term &#8220;cube root&#8221; has a direct connection to the geometry of a cube. If a cube has a side length of&nbsp;q, its volume is calculated as length times width times height, or&nbsp;q \u00d7 q \u00d7 q, which simplifies to&nbsp;q\u00b3. In the context of this problem, you can imagine we are given a cube with a volume of 125 cubic units, and we need to determine the length of one of its sides, which is&nbsp;q.<\/p>\n\n\n\n<p>To find this value, we can search for a number that, when used as a factor three times, results in a product of 125. A good strategy is to test small, positive integers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\u00b3 = 1 \u00d7 1 \u00d7 1 = 1<\/li>\n\n\n\n<li>2\u00b3 = 2 \u00d7 2 \u00d7 2 = 8<\/li>\n\n\n\n<li>3\u00b3 = 3 \u00d7 3 \u00d7 3 = 27<\/li>\n\n\n\n<li>4\u00b3 = 4 \u00d7 4 \u00d7 4 = 64<\/li>\n<\/ul>\n\n\n\n<p>These results are all smaller than 125. Let&#8217;s test the next whole number, 5:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5\u00b3 = 5 \u00d7 5 \u00d7 5 = 125<\/li>\n<\/ul>\n\n\n\n<p>This calculation provides the correct result. When we substitute 5 for&nbsp;q&nbsp;in the original equation, we get&nbsp;5\u00b3 = 125, which is a true statement. Therefore, the solution to the equation is&nbsp;q = 5. The cube root of 125 is 5. This is the unique real number solution to the equation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner6-76.jpeg\" alt=\"\" class=\"wp-image-280964\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: q = 5 The equation presented is&nbsp;q\u00b3 = 125. To solve for&nbsp;q, we need to understand what this equation represents. The term&nbsp;q\u00b3&nbsp;signifies&nbsp;q&nbsp;raised to the third power, which is the mathematical operation of multiplying&nbsp;q&nbsp;by itself three times (q \u00d7 q \u00d7 q). The problem asks us to find the specific [&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-280962","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280962","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=280962"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280962\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280962"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280962"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}