{"id":17038,"date":"2025-06-12T07:25:00","date_gmt":"2025-06-12T07:25:00","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=17038"},"modified":"2025-06-12T07:25:02","modified_gmt":"2025-06-12T07:25:02","slug":"benjamin-writes-an-expression-for-the-sum-of-1-cubed-2-cubed-and-3-cubed","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/benjamin-writes-an-expression-for-the-sum-of-1-cubed-2-cubed-and-3-cubed\/","title":{"rendered":"benjamin writes an expression for the sum of 1 cubed, 2 cubed, and 3 cubed"},"content":{"rendered":"\n<p>benjamin writes an expression for the sum of 1 cubed, 2 cubed, and 3 cubed. What is the value of the expression<\/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><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<p>The expression for the sum of 1 cubed, 2 cubed, and 3 cubed is: 13+23+33=1+8+27=361^3 + 2^3 + 3^3 = 1 + 8 + 27 = \\boxed{36}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (300 words):<\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to evaluate the sum of three <strong>cube numbers<\/strong>. A cube number is the result of multiplying a number by itself three times. Mathematically, we express this as n3=n\u00d7n\u00d7nn^3 = n \\times n \\times n.<\/p>\n\n\n\n<p>Benjamin writes the expression: 13+23+331^3 + 2^3 + 3^3<\/p>\n\n\n\n<p>Let\u2019s solve each term one at a time:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>13=1\u00d71\u00d71=11^3 = 1 \\times 1 \\times 1 = 1<\/li>\n\n\n\n<li>23=2\u00d72\u00d72=82^3 = 2 \\times 2 \\times 2 = 8<\/li>\n\n\n\n<li>33=3\u00d73\u00d73=273^3 = 3 \\times 3 \\times 3 = 27<\/li>\n<\/ol>\n\n\n\n<p>Now we add the results of each cube: 1+8+27=361 + 8 + 27 = 36<\/p>\n\n\n\n<p>So, the <strong>value of the expression is 36<\/strong>.<\/p>\n\n\n\n<p>This type of problem helps students understand how exponents work, particularly cubed numbers (also called &#8220;third powers&#8221;). It also demonstrates how math operations can be broken into steps\u2014first by evaluating each cube and then adding them together.<\/p>\n\n\n\n<p>An interesting fact is that the sum of the cubes of the first <em>n<\/em> natural numbers has a neat formula: 13+23+33+\u22ef+n3=(n(n+1)2)21^3 + 2^3 + 3^3 + \\dots + n^3 = \\left( \\frac{n(n+1)}{2} \\right)^2<\/p>\n\n\n\n<p>If we apply it with n=3n = 3: (3(3+1)2)2=(122)2=62=36\\left( \\frac{3(3+1)}{2} \\right)^2 = \\left( \\frac{12}{2} \\right)^2 = 6^2 = 36<\/p>\n\n\n\n<p>This confirms our answer. This formula is useful when working with larger sets of numbers.<\/p>\n\n\n\n<p>In summary, Benjamin\u2019s expression equals 36, and it teaches valuable concepts like exponentiation, order of operations, and number patterns in mathematics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>benjamin writes an expression for the sum of 1 cubed, 2 cubed, and 3 cubed. What is the value of the expression The correct answer and explanation is: Correct Answer: The expression for the sum of 1 cubed, 2 cubed, and 3 cubed is: 13+23+33=1+8+27=361^3 + 2^3 + 3^3 = 1 + 8 + 27 [&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-17038","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17038","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=17038"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17038\/revisions"}],"predecessor-version":[{"id":17039,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17038\/revisions\/17039"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=17038"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=17038"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=17038"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}