{"id":248737,"date":"2025-07-08T17:43:15","date_gmt":"2025-07-08T17:43:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248737"},"modified":"2025-07-08T17:43:17","modified_gmt":"2025-07-08T17:43:17","slug":"the-solution-to-the-equation-x364-is-called-the-cube-root-of-64-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/the-solution-to-the-equation-x364-is-called-the-cube-root-of-64-2\/","title":{"rendered":"The solution to the equation\u00a0x3=64\u00a0is called the cube root of 64."},"content":{"rendered":"\n
The solution to the equation\u00a0x3=64\u00a0is called the cube root of 64.<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Here are the correct answers and the explanation for each expression.<\/p>\n\n\n\n
Correct Answer:<\/strong>
a. 4
b. 5
c. -2<\/p>\n\n\n\n
Explanation<\/h3>\n\n\n\n
The problem asks us to evaluate three different cube roots based on the provided definition. A cube root is the number that, when multiplied by itself three times, results in the number under the radical symbol. This is the inverse operation of cubing a number.<\/p>\n\n\n\n
a. \u00b3\u221a64<\/strong><\/p>\n\n\n\n
To find the cube root of 64, we need to find a number, let’s call it x, such that x\u00b3 = 64. We are looking for the number that when used as a factor three times equals 64. We can test small integers to find the solution. We know 2 \u00d7 2 \u00d7 2 = 8, which is too small. Let’s try 3: 3 \u00d7 3 \u00d7 3 = 27, still too small. Let’s try 4: 4 \u00d7 4 = 16, and 16 \u00d7 4 = 64. Since 4\u00b3 = 64, the cube root of 64 is 4.<\/p>\n\n\n\n
b. \u00b3\u221a125<\/strong><\/p>\n\n\n\n
Following the same logic, we are looking for a number that, when cubed, equals 125. From our previous calculation, we know 4\u00b3 is 64, so we should try the next whole number, which is 5. Let’s calculate 5\u00b3. The calculation is 5 \u00d7 5 \u00d7 5. First, 5 \u00d7 5 = 25. Then, 25 \u00d7 5 = 125. Because 5\u00b3 = 125, we have found that the cube root of 125 is 5.<\/p>\n\n\n\n
c. \u00b3\u221a-8<\/strong><\/p>\n\n\n\n
This problem involves finding the cube root of a negative number. Unlike square roots, it is possible to find a real cube root for a negative number. The logic remains the same: we need a number x where x\u00b3 = -8. Since the result is negative, the number we are looking for must also be negative. A positive number cubed always yields a positive result. Let’s test small negative integers. We can try -2. The calculation would be (-2) \u00d7 (-2) \u00d7 (-2). First, (-2) \u00d7 (-2) = 4. Then, we multiply this result by -2, so 4 \u00d7 (-2) = -8. Since (-2)\u00b3 = -8, the cube root of -8 is -2.<\/p>\n\n\n\n
\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
The solution to the equation\u00a0x3=64\u00a0is called the cube root of 64. The Correct Answer and Explanation is: Here are the correct answers and the explanation for each expression. Correct Answer:a. 4b. 5c. -2 Explanation The problem asks us to evaluate three different cube roots based on the provided definition. A cube root is the number […]<\/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-248737","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248737","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=248737"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248737\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}