{"id":25913,"date":"2023-03-06T11:07:50","date_gmt":"2023-03-06T11:07:50","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=25913"},"modified":"2024-04-02T07:06:51","modified_gmt":"2024-04-02T07:06:51","slug":"perfect-cube-of-numbers-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube","title":{"rendered":"Perfect Cube of Numbers: Definition, List, Chart, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-7510f9ff-ca70-4524-ba16-f1f971460c86\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube#0-what-are-perfect-cubes>What Are Perfect Cubes<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube#4-how-to-find-a-perfect-cube>How to Find a Perfect Cube<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube#5-perfect-cube-formula>Perfect Cube Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube#9-solved-examples-on-perfect-cubes>Solved Examples on Perfect Cubes<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube#10-practice-problems-on-perfect-cubes>Practice Problems on Perfect Cubes<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube#11-frequently-asked-questions-on-perfect-cubes>Frequently Asked Questions on Perfect Cubes<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-perfect-cubes\">What Are Perfect Cubes<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>When we multiply the same integer thrice, the number we get is called a perfect cube number.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, if we multiply the number 2 thrice, the product is 8.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, 8 is a perfect cube.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2 \\times 2 \\times 2 = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here are a few examples of perfect cubes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"696\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/perfect-cubes-of-the-numbers-1-to-10.png\" alt=\"Perfect cubes of the numbers 1 to 10\" class=\"wp-image-41499\" title=\"Perfect cubes of the numbers 1 to 10\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/perfect-cubes-of-the-numbers-1-to-10.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/perfect-cubes-of-the-numbers-1-to-10-268x300.png 268w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-perfect-cube-definition\">Perfect Cube: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>If a number can be decomposed into a product of the same three integers, it is known as a perfect cube<\/strong>. In other words, if the cube root of a number is an integer, then the number can be considered as a perfect cube.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If x is a perfect cube of y, then we represent it as $x = y^{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, in other words, the cube root of x is y.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We write it as $^{3}\\sqrt{x}= y$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We write <strong>\u201cn cubed\u201d as <\/strong>$n^{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Perfect cube examples:<\/strong> $1^{3} = 1, 2^{3} = 8, 3^{3} = 27, 5^{3} = 125,$ etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Note that we can find a cube of any number, whether it is an integer or a decimal, or a fraction.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, the cube of 0.2 is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$0.2 \\times 0.2 \\times 0.2=0.008$<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-volume-using-unit-cubes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_vol_unit_cubes_2_pt.png\" alt=\"Find the Volume using Unit Cubes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Volume using Unit Cubes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-cones-and-cubes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_cones_cubes_pt.png\" alt=\"Identify Cones and Cubes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Cones and Cubes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/make-a-number-using-cubes-up-to-5\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_make_num_w5_pt.png\" alt=\"Make a Number Using Cubes (Up to 5) Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Make a Number Using Cubes (Up to 5) Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/making-a-number-up-to-10-using-cubes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_make_num_w10_pt.png\" alt=\"Making a Number (Up to 10) Using Cubes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Making a Number (Up to 10) Using Cubes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-list-of-perfect-cubes-1-to-50\">List of Perfect Cubes 1 to 50<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The table given below shows the list of perfect cubes we get if we multiply natural numbers $(1\\;\u2013\\;50)$ thrice.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Perfect Cubes Chart<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td><strong>Number&nbsp;<\/strong><\/td><td><strong>Multiplied Thrice<\/strong><\/td><td><strong>Perfect Cubes<\/strong><\/td><td><\/td><td><strong>Number&nbsp;<\/strong><\/td><td><strong>Multiplied Thrice<\/strong><\/td><td><strong>Perfect Cubes<\/strong><\/td><\/tr><tr><td><strong>1<\/strong><\/td><td>$1 \\times 1 \\times 1$<\/td><td><strong>1<\/strong><\/td><td><\/td><td><strong>26<\/strong><\/td><td>$26 \\times 26 \\times 26$<\/td><td><strong>17576<\/strong><\/td><\/tr><tr><td><strong>2<\/strong><\/td><td>$2 \\times 2 \\times 2$<\/td><td><strong>8<\/strong><\/td><td><\/td><td><strong>27<\/strong><\/td><td>$27 \\times 27 \\times 27$<\/td><td><strong>19683<\/strong><\/td><\/tr><tr><td><strong>3<\/strong><\/td><td>$3 \\times 3 \\times 3$<\/td><td><strong>27<\/strong><\/td><td><\/td><td><strong>28<\/strong><\/td><td>$28 \\times 28 \\times 28$<\/td><td><strong>21952<\/strong><\/td><\/tr><tr><td><strong>4<\/strong><\/td><td>$4 \\times 4 \\times 4$<\/td><td><strong>64<\/strong><\/td><td><\/td><td><strong>29<\/strong><\/td><td>$29 \\times 29 \\times 29$<\/td><td><strong>24389<\/strong><\/td><\/tr><tr><td><strong>5<\/strong><\/td><td>$5 \\times 5 \\times 5$<\/td><td><strong>125<\/strong><\/td><td><\/td><td><strong>30<\/strong><\/td><td>$30 \\times 30 \\times 30$<\/td><td><strong>27000<\/strong><\/td><\/tr><tr><td><strong>6<\/strong><\/td><td>$6 \\times 6 \\times 6$<\/td><td><strong>216<\/strong><\/td><td><\/td><td><strong>31<\/strong><\/td><td>$31 \\times 31 \\times 31$<\/td><td><strong>29791<\/strong><\/td><\/tr><tr><td><strong>7<\/strong><\/td><td>$7 \\times 7 \\times 7$<\/td><td><strong>343<\/strong><\/td><td><\/td><td><strong>32<\/strong><\/td><td>$32 \\times 32 \\times 32$<\/td><td><strong>32768<\/strong><\/td><\/tr><tr><td><strong>8<\/strong><\/td><td>$8 \\times 8 \\times 8$<\/td><td><strong>512<\/strong><\/td><td><\/td><td><strong>33<\/strong><\/td><td>$33 \\times 33 \\times 33$<\/td><td><strong>35937<\/strong><\/td><\/tr><tr><td><strong>9<\/strong><\/td><td>$9 \\times 9 \\times 9$<\/td><td><strong>729<\/strong><\/td><td><\/td><td><strong>34<\/strong><\/td><td>$34 \\times 34 \\times 34$<\/td><td><strong>39304<\/strong><\/td><\/tr><tr><td><strong>10<\/strong><\/td><td>$10 \\times 10 \\times 10$<\/td><td><strong>1000<\/strong><\/td><td><\/td><td><strong>35<\/strong><\/td><td>$35 \\times 35 \\times 35$<\/td><td><strong>42875<\/strong><\/td><\/tr><tr><td><strong>11<\/strong><\/td><td>$11 \\times 11 \\times 11$<\/td><td><strong>1331<\/strong><\/td><td><\/td><td><strong>36<\/strong><\/td><td>$36 \\times 36 \\times 36$<\/td><td><strong>46656<\/strong><\/td><\/tr><tr><td><strong>12<\/strong><\/td><td>$12 \\times 12 \\times 12$<\/td><td><strong>1728<\/strong><\/td><td><\/td><td><strong>37<\/strong><\/td><td>$37 \\times 37 \\times 37$<\/td><td><strong>50653<\/strong><\/td><\/tr><tr><td><strong>13<\/strong><\/td><td>$13 \\times 13 \\times 13$<\/td><td><strong>2197<\/strong><\/td><td><\/td><td><strong>38<\/strong><\/td><td>$38 \\times 38 \\times 38$<\/td><td><strong>54872<\/strong><\/td><\/tr><tr><td><strong>14<\/strong><\/td><td>$14 \\times 14 \\times 14$<\/td><td><strong>2744<\/strong><\/td><td><\/td><td><strong>39<\/strong><\/td><td>$39 \\times 39 \\times 39$<\/td><td><strong>59319<\/strong><\/td><\/tr><tr><td><strong>15<\/strong><\/td><td>$15 \\times 15 \\times 15$<\/td><td><strong>3375<\/strong><\/td><td><\/td><td><strong>40<\/strong><\/td><td>$40 \\times 40 \\times 40$<\/td><td><strong>64000<\/strong><\/td><\/tr><tr><td><strong>16<\/strong><\/td><td>$16 \\times 16 \\times 16$<\/td><td><strong>4096<\/strong><\/td><td><\/td><td><strong>41<\/strong><\/td><td>$41 \\times 41 \\times 41$<\/td><td><strong>68921<\/strong><\/td><\/tr><tr><td><strong>17<\/strong><\/td><td>$17 \\times 17 \\times 17$<\/td><td><strong>4913<\/strong><\/td><td><\/td><td><strong>42<\/strong><\/td><td>$42 \\times 42 \\times 42$<\/td><td><strong>74088<\/strong><\/td><\/tr><tr><td><strong>18<\/strong><\/td><td>$18 \\times 18 \\times 18$<\/td><td><strong>5832<\/strong><\/td><td><\/td><td><strong>43<\/strong><\/td><td>$43 \\times 43 \\times 43$<\/td><td><strong>79507<\/strong><\/td><\/tr><tr><td><strong>19<\/strong><\/td><td>$19 \\times 19 \\times 19$<\/td><td><strong>6859<\/strong><\/td><td><\/td><td><strong>44<\/strong><\/td><td>$44 \\times 44 \\times 44$<\/td><td><strong>85184<\/strong><\/td><\/tr><tr><td><strong>20<\/strong><\/td><td>$20 \\times 20 \\times 20$<\/td><td><strong>8000<\/strong><\/td><td><\/td><td><strong>45<\/strong><\/td><td>$45 \\times 45 \\times 45$<\/td><td><strong>91125<\/strong><\/td><\/tr><tr><td><strong>21<\/strong><\/td><td>$21 \\times 21 \\times 21$<\/td><td><strong>9261<\/strong><\/td><td><\/td><td><strong>46<\/strong><\/td><td>$46 \\times 46 \\times 46$<\/td><td><strong>97336<\/strong><\/td><\/tr><tr><td><strong>22<\/strong><\/td><td>$22 \\times 22 \\times 22$<\/td><td><strong>10648<\/strong><\/td><td><\/td><td><strong>47<\/strong><\/td><td>$47 \\times 47 \\times 47$<\/td><td><strong>103823<\/strong><\/td><\/tr><tr><td><strong>23<\/strong><\/td><td>$23 \\times 23 \\times 23$<\/td><td><strong>12167<\/strong><\/td><td><\/td><td><strong>48<\/strong><\/td><td>$48 \\times 48 \\times 48$<\/td><td><strong>110592<\/strong><\/td><\/tr><tr><td><strong>24<\/strong><\/td><td>$24 \\times 24 \\times 24$<\/td><td><strong>13824<\/strong><\/td><td><\/td><td><strong>49<\/strong><\/td><td>$49 \\times 49 \\times 49$<\/td><td><strong>117649<\/strong><\/td><\/tr><tr><td><strong>25<\/strong><\/td><td>$25 \\times 25 \\times 25$<\/td><td><strong>15625<\/strong><\/td><td><\/td><td><strong>50<\/strong><\/td><td>$50 \\times 50 \\times 50$<\/td><td><strong>125000<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/cylinders-and-cubes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/cylinders-and-cubes.jpeg\" alt=\"Cylinders and Cubes Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-cube-root-of-perfect-cubes\">Cube Root of Perfect Cubes<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When we multiply a number three times by itself, we say that the number is \u201ccubed.\u201d To find the cube root of a number, we need to reverse the process of cubing a number. For example:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When the number 3 is cubed, we get $3 \\times 3 \\times 3$, which is 27. The cube root of 27 is 3. This is because we get 27 on multiplying the number 3 three times. The <strong>symbol for cube root is <\/strong>$^{3}\\sqrt{}$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we want to express this in exponent form, we write it as:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Cube root of a number $= (number)^{\\frac{1}{3}}$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"424\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/cube-root-of-x-symbol.png\" alt=\"Cube root of x symbol\" class=\"wp-image-41500\" title=\"Cube root of x symbol\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/cube-root-of-x-symbol.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/cube-root-of-x-symbol-300x205.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-find-a-perfect-cube\">How to Find a Perfect Cube<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Every composite number can be expressed as the product of the power of its prime factors. If the power of all the prime factors is in the multiple of 3, then the number is known as a perfect cube. Each prime factor of a number appears three times in the prime factorization of its cube.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1:<\/strong> Find the prime factorization of the given number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2:<\/strong> Club all the same factors together.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3:<\/strong> Repeat the above step for all the sets of the group of the same three factors. If some factors are left behind, then we conclude that the given number is not a perfect cube. Otherwise, the given number is a perfect cube.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us take the following example to understand this.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1:<\/strong> Check if 2197 is a perfect cube number?<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us first find the prime factorization of 2197.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2197 = 13 \\times 13 \\times 13 = 13^{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, 2197 is a perfect cube of 13.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2: Is 216 a perfect cube?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/prime-factorization-of-216-using-division-method.png\" alt=\"Prime factorization of 216 using division method\" class=\"wp-image-41501\" title=\"Prime factorization of 216 using division method\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/prime-factorization-of-216-using-division-method.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/prime-factorization-of-216-using-division-method-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$216 = (2 \\times2 \\times 2) \\times (3 \\times 3 \\times 3) = 2^{3} \\times 3^{3} = 6^{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, 216 is a perfect cube.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-perfect-cube-formula\">Perfect Cube Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To identify a perfect cube, we use the perfect cube formula. Suppose we have a number, x, such that<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = y \\times y \\times y$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-properties-of-perfect-cubes\">Properties of Perfect Cubes<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">An even number has a cube which is even. For example, $2^{3} = 8$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">An odd number has a cube which is odd. For example, $3^{3} = 27$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">We can express the perfect cube of a number as the sum of consecutive odd numbers.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$1^{3} = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2^{3} = 3 + 5 = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3^{3} = 7 + 9 + 11 = 27$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4^{3} = 13 + 15 + 17 + 19 = 64$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The total count of consecutive odd numbers which sum up to form a perfect cube is equal to the number that is being cubed.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To express $1^{3}$, only 1 odd number is involved.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To express $2^{3}$, it involves the sum of 2 odd numbers, $3 + 5$.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-facts-about-perfect-cube\">Facts about Perfect Cube<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">There are some special perfect cube roots that can be found using the sum of digits of the cube number. For example:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$^{3}\\sqrt{0} = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$^{3}\\sqrt{1} = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$^{3}\\sqrt{512}&nbsp; = 5 + 1 + 2 = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$^{3}\\sqrt{4913} = 4 + 9 + 1 + 3 = 17$ etc.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A cube is a geometric solid whose each side is of the same length.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The volume of a cube with side \u201cs\u201d is given by \u201cs<sup>3<\/sup>\u201d cubic units.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The cube of negative numbers is negative.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: $(\\;-6)^{3} = \\;-\\;216$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about perfect cube numbers, their properties, and formulas. Let\u2019s solve a few examples for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-solved-examples-on-perfect-cubes\">Solved Examples on Perfect Cubes<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Is 27 a perfect cube number?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us find the prime factorization of 27.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$27 = 3 \\times 3 \\times 3$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since we can make one group of 3, i.e., $3^{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, 27 is a perfect cube. Its cube root is 3.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. If the value of <\/strong>$x^{3} = 512$<strong>, find the value of \u201cx\u201d using the perfect cube formula.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The perfect cube formula is $y = ^{3}\\sqrt{x}$, where \u201cx\u201d is the perfect cube, and \u201cy\u201d is the cube root of \u201cx.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given, $x^{3} = 512$, therefore, $y = ^{3}\\sqrt{512}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Prime factorization of $512 = (2 \\times 2 \\times 2) \\times (2 \\times 2 \\times 2) \\times (2 \\times 2 \\times 2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$512 = (2 \\times 2 \\times 2)^{3} = 8^{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $y = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Is 1000 a perfect cube number?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us first look at the prime factorization of 1000.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"140\" height=\"288\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/prime-factorization-of-1000.png\" alt=\"Prime factorization of 1000\" class=\"wp-image-41502\" title=\"Prime factorization of 1000\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$1000 = 2 \\times 2 \\times 2 \\times 5 \\times 5 \\times 5 = 10^{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, 1000 is a perfect cube number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. What is the perfect cube of 20?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiply 20 three times with itself.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The perfect cube of $20 = 20 \\times 20 \\times 20 = 8000$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. What is the cube root of 343?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The prime factorization of 343 is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$343 = 7 \\times 49$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$343 =7 \\times 7 \\times 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$343 = 7^{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the cube root of 343 is 7.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-practice-problems-on-perfect-cubes\">Practice Problems on Perfect Cubes<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Perfect Cube of Numbers: Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">125 is a _____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">perfect square<\/div><div class=\"spq_answer_block\" data-value=\"1\">perfect cube<\/div><div class=\"spq_answer_block\" data-value=\"2\">prime number<\/div><div class=\"spq_answer_block\" data-value=\"3\">none of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: perfect cube<br\/>$125 = 5 \\times 5 \\times 5 = 5^{3}$.<br>\r\nTherefore, 125 is a perfect cube.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If the value of $x^{3} = 729$, what is the value of \u201cx\u201d using the perfect cube formula?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5<\/div><div class=\"spq_answer_block\" data-value=\"1\">6<\/div><div class=\"spq_answer_block\" data-value=\"2\">7<\/div><div class=\"spq_answer_block\" data-value=\"3\">8<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 7<br\/>$729 = 7^{3} = x^{3}$<br>\r\nHence, $x = 7$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the perfect cube of 5?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">120<\/div><div class=\"spq_answer_block\" data-value=\"1\">125<\/div><div class=\"spq_answer_block\" data-value=\"2\">130<\/div><div class=\"spq_answer_block\" data-value=\"3\">135<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 125<br\/>The perfect cube of $5 = 5 \\times 5 \\times 5 =125$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the cube root of 1331?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">11<\/div><div class=\"spq_answer_block\" data-value=\"1\">10<\/div><div class=\"spq_answer_block\" data-value=\"2\">12<\/div><div class=\"spq_answer_block\" data-value=\"3\">13<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 11<br\/>The prime factorization of 1331 is:<br>\r\n$1331 = 11 \\times 11 \\times 11 = 113$<br>\r\nHence, the cube root of 1331 is 11.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which number is a perfect cube among the following options?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">100<\/div><div class=\"spq_answer_block\" data-value=\"1\">44<\/div><div class=\"spq_answer_block\" data-value=\"2\">33<\/div><div class=\"spq_answer_block\" data-value=\"3\">729<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 729<br\/>729 is a perfect cube of 9.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Perfect Cube of Numbers: Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Perfect Cube of Numbers\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n     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       \"name\": \"What is the cube root of 1331?\",\n                    \"text\": \"What is the cube root of 1331?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The prime factorization of 1331 is:<br>\r\n$$1331 = 11 \\\\times 11 \\\\times 11 = 113$$<br>\r\nHence, the cube root of 1331 is 11.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The prime factorization of 1331 is:<br>\r\n$$1331 = 11 \\\\times 11 \\\\times 11 = 113$$<br>\r\nHence, the cube root of 1331 is 11.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The prime factorization of 1331 is:<br>\r\n$$1331 = 11 \\\\times 11 \\\\times 11 = 113$$<br>\r\nHence, the cube root of 1331 is 11.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The prime factorization of 1331 is:<br>\r\n$$1331 = 11 \\\\times 11 \\\\times 11 = 113$$<br>\r\nHence, the cube root of 1331 is 11.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"11\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The prime factorization of 1331 is:<br>\r\n$$1331 = 11 \\\\times 11 \\\\times 11 = 113$$<br>\r\nHence, the cube root of 1331 is 11.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The prime factorization of 1331 is:<br>\r\n$$1331 = 11 \\\\times 11 \\\\times 11 = 113$$<br>\r\nHence, the cube root of 1331 is 11.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which number is a perfect cube among the following options?\",\n                    \"text\": \"Which number is a perfect cube among the following options?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"729 is a perfect cube of 9.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"729 is a perfect cube of 9.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"44\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"729 is a perfect cube of 9.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"33\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"729 is a perfect cube of 9.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"729\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"729 is a perfect cube of 9.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"729 is a perfect cube of 9.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-frequently-asked-questions-on-perfect-cubes\">Frequently Asked Questions on Perfect Cubes<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-085fdba3-e6b6-49a9-8e9d-40e9a823e472\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-085fdba3-e6b6-49a9-8e9d-40e9a823e472\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-085fdba3-e6b6-49a9-8e9d-40e9a823e472\"><strong>Can the perfect cube numbers be negative?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-085fdba3-e6b6-49a9-8e9d-40e9a823e472\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, perfect cubes can be both positive and negative numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, if we multiply the negative integer $-5$, three times, we get $-125$, which is a perfect cube.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-085fdba3-e6b6-49a9-8e9d-40e9a823e472\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-085fdba3-e6b6-49a9-8e9d-40e9a823e472\"><strong>What is the formula for <\/strong>$(a + b)^{3}$<strong>?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-085fdba3-e6b6-49a9-8e9d-40e9a823e472\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(a + b)^{3} = a^{3} + b^{3} + 3a^{2}b + 3ab^{2}$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-085fdba3-e6b6-49a9-8e9d-40e9a823e472\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-085fdba3-e6b6-49a9-8e9d-40e9a823e472\"><strong>What are perfect squares?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-085fdba3-e6b6-49a9-8e9d-40e9a823e472\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A perfect square is a number obtained by multiplying an integer with itself.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-085fdba3-e6b6-49a9-8e9d-40e9a823e472\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-085fdba3-e6b6-49a9-8e9d-40e9a823e472\"><strong>How to factor a perfect cube binomial?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-085fdba3-e6b6-49a9-8e9d-40e9a823e472\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A perfect cube binomial is an expression consisting of two terms that are perfect cubes. We can factor a perfect cube binomial using the formula<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u200b\u200b$a^{3} \\;-\\; b^{3} = (a \\;-\\; b)(a^{2} + ab + b^{2})$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\u200b\u200ba^{3} + b^{3} = (a \\;-\\; b)(a^{2} \\;-\\; ab + b^{2})$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-085fdba3-e6b6-49a9-8e9d-40e9a823e472\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-085fdba3-e6b6-49a9-8e9d-40e9a823e472\"><strong>Is 125 a perfect cube?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-085fdba3-e6b6-49a9-8e9d-40e9a823e472\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, 125 is a cube of 5.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Perfect Cubes When we multiply the same integer thrice, the number we get is called a perfect cube number.&nbsp; For example, if we multiply the number 2 thrice, the product is 8.&nbsp; Therefore, 8 is a perfect cube. $2 \\times 2 \\times 2 = 8$ Here are a few examples of perfect cubes. &#8230; <a title=\"Perfect Cube of Numbers: Definition, List, Chart, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-cube\" aria-label=\"More on Perfect Cube of Numbers: Definition, List, Chart, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-25913","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25913","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=25913"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25913\/revisions"}],"predecessor-version":[{"id":41503,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25913\/revisions\/41503"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=25913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=25913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=25913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}