{"id":16085,"date":"2025-06-10T22:42:14","date_gmt":"2025-06-10T22:42:14","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=16085"},"modified":"2025-06-10T22:42:17","modified_gmt":"2025-06-10T22:42:17","slug":"which-monomial-is-a-perfect-cube","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-monomial-is-a-perfect-cube\/","title":{"rendered":"Which monomial is a perfect cube"},"content":{"rendered":"\n<p>Which monomial is a perfect cube? 1&#215;3 3&#215;3 6&#215;3 9&#215;3<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>The monomial that is a <strong>perfect cube<\/strong> is:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1x\u00b3<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Correct Answer: <strong>1x\u00b3<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd0d Explanation (300 words):<\/h3>\n\n\n\n<p>A <strong>perfect cube<\/strong> is a number or expression that can be written as the cube of another number or expression. In algebraic terms, a monomial is a perfect cube if <strong>both the numerical coefficient and the variable part are perfect cubes<\/strong>.<\/p>\n\n\n\n<p>Let\u2019s analyze each choice:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>1x\u00b3<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1<\/strong> is a perfect cube: 1=131 = 1^3<\/li>\n\n\n\n<li><strong>x\u00b3<\/strong> is a perfect cube: x3=(x)3x^3 = (x)^3<\/li>\n\n\n\n<li>Therefore, 1&#215;3=(1x)31x^3 = (1x)^3<\/li>\n\n\n\n<li>\u2705 <strong>Perfect cube<\/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>3x\u00b3<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3<\/strong> is <strong>not<\/strong> a perfect cube. The cube root of 3 is approximately 1.442, which is not an integer.<\/li>\n\n\n\n<li>Even though <strong>x\u00b3<\/strong> is a perfect cube, the coefficient 3 is not.<\/li>\n\n\n\n<li>\u274c <strong>Not a perfect cube<\/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>6x\u00b3<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>6<\/strong> is not a perfect cube: The cube root of 6 is approximately 1.817, not an integer.<\/li>\n\n\n\n<li><strong>x\u00b3<\/strong> is a perfect cube, but again the coefficient is not.<\/li>\n\n\n\n<li>\u274c <strong>Not a perfect cube<\/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>9x\u00b3<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>9<\/strong> is not a perfect cube: The cube root of 9 is approximately 2.080, not an integer.<\/li>\n\n\n\n<li><strong>x\u00b3<\/strong> is a perfect cube, but 9 is not.<\/li>\n\n\n\n<li>\u274c <strong>Not a perfect cube<\/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\">\ud83d\udd11 Key Concept:<\/h3>\n\n\n\n<p>A monomial like axnax^n is a perfect cube <strong>if and only if<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>aa is a perfect cube (like 1, 8, 27, etc.)<\/li>\n\n\n\n<li>nn is divisible by 3 (so that xnx^n can be written as (xk)3(x^k)^3)<\/li>\n<\/ol>\n\n\n\n<p>Only <strong>1x\u00b3<\/strong> satisfies both conditions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 Final Answer: <strong>1x\u00b3 is the only perfect cube among the given monomials.<\/strong><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Which monomial is a perfect cube? 1&#215;3 3&#215;3 6&#215;3 9&#215;3 The correct answer and explanation is: The monomial that is a perfect cube is: 1x\u00b3 \u2705 Correct Answer: 1x\u00b3 \ud83d\udd0d Explanation (300 words): A perfect cube is a number or expression that can be written as the cube of another number or expression. In algebraic [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-16085","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16085","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=16085"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16085\/revisions"}],"predecessor-version":[{"id":16087,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16085\/revisions\/16087"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}