{"id":839851,"date":"2024-08-09T13:53:58","date_gmt":"2024-08-09T08:23:58","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=839851"},"modified":"2024-08-09T13:53:58","modified_gmt":"2024-08-09T08:23:58","slug":"exam-prep-all-perfect-cube-numbers","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-all-perfect-cube-numbers\/","title":{"rendered":"All Perfect Cube Numbers: Definition, Steps, Properties, and Solved Examples"},"content":{"rendered":"\n<p>A perfect cube is a number that can be expressed as the product of an integer multiplied by itself twice, symbolically represented as<strong> n = x<sup>3<\/sup><\/strong>, where x is an integer. Understanding perfect cubes is fundamental in mathematics, particularly in <a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-algebraic-identities\/\"><strong>algebra<\/strong><\/a> and number theory. This article delves into the concept of perfect cube numbers, offering a comprehensive definition, step-by-step methods for identifying them, and a detailed explanation of their properties. Additionally, you&#8217;ll find a complete list of perfect cubes, alongside solved examples to solidify your grasp of the topic. Whether you&#8217;re a student or an aspirant, this guide will enhance your understanding of perfect cubes and their applications.<\/p>\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-definition-of-perfect-cube\">Definition of Perfect Cube<\/h2>\n\n\n\n<p>A perfect cube is a number that is the result of an integer multiplied by itself twice. In other words, a number n is a perfect cube if there exists an integer x such that:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>n = x<\/strong><strong><sup>3<\/sup><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Here, x is the cube root of n, and n is said to be a perfect cube.<\/p>\n\n\n\n<p><strong>Integer Cube Root<\/strong>: A perfect cube always has an integer cube root. If n is a perfect cube, then <strong><sup>3<\/sup><\/strong><strong>\u221ax = x<\/strong><strong><sup>1\/3<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Odd and Even Properties<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The cube of an even integer is even. For example, 2<sup>3<\/sup> = 8 is even.<\/li>\n\n\n\n<li>The cube of an odd integer is odd. For example, 3<sup>3 <\/sup>= 27 is odd.<\/li>\n<\/ul>\n\n\n\n<p><strong>The sum of Consecutive Odd Numbers<\/strong>: Every perfect cube can be represented as the sum of a series of consecutive odd numbers. For instance, 3<sup>3 <\/sup>= 27 = 7+9+11.<\/p>\n\n\n\n<p><strong>Digit Pattern<\/strong>: The last digit of a perfect cube has a predictable pattern depending on the last digit of its root. For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the last digit of x is 2, then the last digit of x<sup>3<\/sup> will be 8.<\/li>\n\n\n\n<li>If the last digit of x is 7, then the last digit of x<sup>3<\/sup> will be 3.<\/li>\n<\/ul>\n\n\n\n<p><strong>Non-Negative Results<\/strong>: The cube of any non-negative integer is non-negative, meaning x<sup>3 <\/sup>\u2265 0 for any integer x.<\/p>\n\n\n\n<p><strong>Scaling Property<\/strong>: If a number n is a perfect cube, then any number of the form K<sup>3<\/sup>\u00d7n (where k is an integer) will also be a perfect cube.<\/p>\n\n\n\n<p><strong>Factorization<\/strong>: The prime factorization of a perfect cube will have each prime factor raised to an exponent that is a multiple of 3. For example, 216 = 2<sup>3<\/sup>\u00d73<sup>3<\/sup> is a perfect cube because both exponents (3 and 3) are multiples of 3.<\/p>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background has-medium-font-size\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-ascending-order\/\"><strong>Ascending Order<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-steps-to-find-the-perfect-cube\">Steps to Find the Perfect Cube<\/h2>\n\n\n\n<p>To determine if a number is a perfect cube or to find the cube of a number, follow these steps:<\/p>\n\n\n\n<p><strong>1. Understand the Concept of Cubing<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The cube of a number xxx is found by multiplying the number by itself twice: x<sup>3 <\/sup>= x \u00d7 x \u00d7 x<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Identify the Number<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Determine the number x whose cube you want to find or verify if a given number n is a perfect cube.<\/li>\n<\/ul>\n\n\n\n<p><strong>3. Calculate the Cube<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>If given x<\/strong>: Compute x<sup>3<\/sup> by multiplying x by itself twice. For example, for x=4, calculate:&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>4<sup>3 <\/sup>= 4\u00d74\u00d74=64<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If given n: To check if n is a perfect cube, find its cube root <sup>3<\/sup>\u221an. If <sup>3<\/sup>\u221an is an integer, then n is a perfect cube. For example, to check if 27 is a perfect cube, calculate:&nbsp;<\/li>\n<\/ul>\n\n\n\n<p><sup>3<\/sup>\u221a27 = 3 (since 3<sup>3 <\/sup>= 27)<\/p>\n\n\n\n<p>Therefore, 27 is a perfect cube.<\/p>\n\n\n\n<p><strong>4. Check the Integer Property<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If calculating the cube root, ensure the result is an integer. If it is not an integer, the number is not a perfect cube.<\/li>\n<\/ul>\n\n\n\n<p><strong>5. Verify Using Prime Factorization (Optional)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factorize the number into its prime factors. For the number to be a perfect cube, each prime factor must appear with an exponent that is a multiple of 3. For example, consider n=216&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>216 = 2<sup>3<\/sup> x 3<sup>3<\/sup><\/p>\n\n\n\n<p>Since the exponents of both prime factors (2 and 3) are multiples of 3, 216 is a perfect cube.<\/p>\n\n\n\n<p><strong>6. Compare with a List of Known Perfect Cubes (Optional)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>You can also compare the number with a pre-existing list of perfect cubes (e.g., 1, 8, 27, 64, 125, etc.) to verify if it is a perfect cube.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-properties-of-perfect-cube\">Properties of Perfect Cube<\/h2>\n\n\n\n<p>Here is the list of properties of the perfect cube.<\/p>\n\n\n\n<p><strong>Integer Cube Root<\/strong>:<\/p>\n\n\n\n<p>A perfect cube has an integer cube root. If n is a perfect cube, then <strong><sup>3<\/sup><\/strong><strong>\u221a27 = 3, <\/strong>because 27 = 3<sup>3<\/sup><\/p>\n\n\n\n<p><strong>Odd and Even Cubes<\/strong>:<\/p>\n\n\n\n<p>The cube of an even integer is even. For example, 4<sup>3 <\/sup>= 64 is even.<\/p>\n\n\n\n<p>The cube of an odd integer is odd. For example, 5<sup>3 <\/sup>= 125 is odd.<\/p>\n\n\n\n<p><strong>The sum of Consecutive Odd Numbers<\/strong>:<\/p>\n\n\n\n<p>Every perfect cube can be expressed as the sum of consecutive odd numbers. For example, 3<sup>3 <\/sup>= 27 = 7+9+11.<\/p>\n\n\n\n<p><strong>Digit Patterns<\/strong>:<\/p>\n\n\n\n<p>The last digit of a perfect cube follows specific patterns depending on the last digit of the base number. For example:<\/p>\n\n\n\n<p>If x ends in 1, x<sup>3 <\/sup>ends in 1.<\/p>\n\n\n\n<p>If x ends in 2, x<sup>3<\/sup> ends in 8.<\/p>\n\n\n\n<p>If x ends in 7, x<sup>3 <\/sup>ends in 3.<\/p>\n\n\n\n<p>If x ends in 9, x<sup>3<\/sup> ends in 9.<\/p>\n\n\n\n<p><strong>Non-Negative Results<\/strong>:<\/p>\n\n\n\n<p>The cube of any non-negative integer is non-negative. Thus, x<sup>3 <\/sup>\u2265 0 for any integer x. For example, (\u22123)<sup>3 <\/sup>= \u221227, and 4<sup>3 <\/sup>= 64.<\/p>\n\n\n\n<p><strong>Scaling Property<\/strong>:<\/p>\n\n\n\n<p>If a number n is a perfect cube, then any number of the form k<sup>3<\/sup>\u00d7n (where k is an integer) is also a perfect cube. For example, if n=8 (which is 2<sup>3<\/sup>), then (3<sup>3<\/sup>)\u00d78 = 216 is also a perfect cube.<\/p>\n\n\n\n<p><strong>Prime Factorization<\/strong>:<\/p>\n\n\n\n<p>The prime factorization of a perfect cube will show each prime factor raised to an exponent that is a multiple of 3. For example, the prime factorization of 216 = 2<sup>3<\/sup>\u00d73<sup>3<\/sup>, indicating it is a perfect cube.<\/p>\n\n\n\n<p><strong>Volume Representation<\/strong>:<\/p>\n\n\n\n<p>A perfect cube can represent the volume of a cube in geometry, where the side length of the cube is an integer. For instance, a cube with a side length of 3 has a volume of 3<sup>3 <\/sup>= 27.<\/p>\n\n\n\n<p><strong>Cube Root Functionality<\/strong>:<\/p>\n\n\n\n<p>The cube root function is the inverse of the cubing function. This property allows the calculation of the original number from its cube. If n = x<sup>3<\/sup>, then x = <sup>3<\/sup>\u221an<\/p>\n\n\n\n<p><strong>Geometric Growth<\/strong>:<\/p>\n\n\n\n<p>Cubing a number results in rapid growth compared to squaring it. For instance, 2<sup>2 <\/sup>= 4 and 2<sup>3 <\/sup>= 8, but 10<sup>2 <\/sup>= 100 and 10<sup>3<\/sup>=1000. This property is important in various fields, including volume calculations and higher-dimensional analysis.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-list-of-perfect-cubes-up-to-1000\">List of Perfect Cubes up to 1000<\/h2>\n\n\n\n<p>Here is a table of the first 50 perfect cubes:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>n<\/strong><\/td><td><strong>n<\/strong><strong><sup>3<\/sup><\/strong><\/td><td><strong>n<\/strong><\/td><td><strong>n<\/strong><strong><sup>3<\/sup><\/strong><\/td><\/tr><tr><td><strong>1<\/strong><\/td><td>1<\/td><td><strong>26<\/strong><\/td><td>17576<\/td><\/tr><tr><td><strong>2<\/strong><\/td><td>8<\/td><td><strong>27<\/strong><\/td><td>19683<\/td><\/tr><tr><td><strong>3<\/strong><\/td><td>27<\/td><td><strong>28<\/strong><\/td><td>21952<\/td><\/tr><tr><td><strong>4<\/strong><\/td><td>64<\/td><td><strong>29<\/strong><\/td><td>24389<\/td><\/tr><tr><td><strong>5<\/strong><\/td><td>125<\/td><td><strong>30<\/strong><\/td><td>27000<\/td><\/tr><tr><td><strong>6<\/strong><\/td><td>216<\/td><td><strong>31<\/strong><\/td><td>29791<\/td><\/tr><tr><td><strong>7<\/strong><\/td><td>343<\/td><td><strong>32<\/strong><\/td><td>32768<\/td><\/tr><tr><td><strong>8<\/strong><\/td><td>512<\/td><td><strong>33<\/strong><\/td><td>35937<\/td><\/tr><tr><td><strong>9<\/strong><\/td><td>729<\/td><td><strong>34<\/strong><\/td><td>39304<\/td><\/tr><tr><td><strong>10<\/strong><\/td><td>1000<\/td><td><strong>35<\/strong><\/td><td>42875<\/td><\/tr><tr><td><strong>11<\/strong><\/td><td>1331<\/td><td><strong>36<\/strong><\/td><td>46656<\/td><\/tr><tr><td><strong>12<\/strong><\/td><td>1728<\/td><td><strong>37<\/strong><\/td><td>50653<\/td><\/tr><tr><td><strong>13<\/strong><\/td><td>2197<\/td><td><strong>38<\/strong><\/td><td>54872<\/td><\/tr><tr><td><strong>14<\/strong><\/td><td>2744<\/td><td><strong>39<\/strong><\/td><td>59319<\/td><\/tr><tr><td><strong>15<\/strong><\/td><td>3375<\/td><td><strong>40<\/strong><\/td><td>64000<\/td><\/tr><tr><td><strong>16<\/strong><\/td><td>4096<\/td><td><strong>41<\/strong><\/td><td>68921<\/td><\/tr><tr><td><strong>17<\/strong><\/td><td>4913<\/td><td><strong>42<\/strong><\/td><td>74088<\/td><\/tr><tr><td><strong>18<\/strong><\/td><td>5832<\/td><td><strong>43<\/strong><\/td><td>79507<\/td><\/tr><tr><td><strong>19<\/strong><\/td><td>6859<\/td><td><strong>44<\/strong><\/td><td>85184<\/td><\/tr><tr><td><strong>20<\/strong><\/td><td>8000<\/td><td><strong>45<\/strong><\/td><td>91125<\/td><\/tr><tr><td><strong>21<\/strong><\/td><td>9261<\/td><td><strong>46<\/strong><\/td><td>97336<\/td><\/tr><tr><td><strong>22<\/strong><\/td><td>10648<\/td><td><strong>47<\/strong><\/td><td>103823<\/td><\/tr><tr><td><strong>23<\/strong><\/td><td>12167<\/td><td><strong>48<\/strong><\/td><td>110592<\/td><\/tr><tr><td><strong>24<\/strong><\/td><td>13824<\/td><td><strong>49<\/strong><\/td><td>117649<\/td><\/tr><tr><td><strong>25<\/strong><\/td><td>15625<\/td><td><strong>50<\/strong><\/td><td>125000<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-perfect-cube-numbers-solved-example\">Perfect Cube Numbers Solved Example<\/h2>\n\n\n\n<p>Here are five solved examples involving perfect cube numbers:<\/p>\n\n\n\n<p><strong>Example 1: Finding the Cube of a Number<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> Find the cube of 7.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>The cube of a number n is calculated by multiplying the number by itself twice:<\/p>\n\n\n\n<p>7<sup>3 <\/sup>= 7\u00d77\u00d77 = 49\u00d77 = 343<\/p>\n\n\n\n<p><strong>Answer:<\/strong> The cube of 7 is 343.<\/p>\n\n\n\n<p><strong>Example 2: Checking if a Number is a Perfect Cube<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> Determine if 729 is a perfect cube.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>To check if 729 is a perfect cube, find its cube root:<\/p>\n\n\n\n<p><sup>3<\/sup>\u221a729 = 9<\/p>\n\n\n\n<p>Since 9 is an integer and 9<sup>3 <\/sup>= 729 is a perfect cube.<\/p>\n\n\n\n<p><strong>Answer:<\/strong> Yes, 729 is a perfect cube.<\/p>\n\n\n\n<p><strong>Example 3: Expressing a Perfect Cube as a Sum of Consecutive Odd Numbers<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> Express 4<sup>3<\/sup> as a sum of consecutive odd numbers.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>First, calculate 4<sup>3<\/sup>:<\/p>\n\n\n\n<p>4<sup>3 <\/sup>= 64<\/p>\n\n\n\n<p>Now, express 64 as a sum of consecutive odd numbers:<\/p>\n\n\n\n<p>64 = 13+15+17+19<\/p>\n\n\n\n<p><strong>Answer:<\/strong> 4<sup>3 <\/sup>= 64 can be expressed as 13+15+17+19.<\/p>\n\n\n\n<p><strong>Example 4: Finding a Number Given its Cube<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> If the cube of a number is 512, what is the number?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>Find the cube root of 512:<\/p>\n\n\n\n<p><sup>3<\/sup>\u221a512 = 8<\/p>\n\n\n\n<p>Since 8<sup>3 <\/sup>= 512, the number is 8.<br><strong>Answer:<\/strong> The number is 8.<\/p>\n\n\n\n<p><strong>Example 5: Solving a Word Problem Involving a Cube<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> A cube-shaped box has a volume of 343 cubic units. What is the length of one side of the box?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>The volume V of a cube is given by V = s<sup>3<\/sup>, where sss is the side length. Given V=343, find s:<\/p>\n\n\n\n<p>S = <sup>3<\/sup>\u221a343 = 7<\/p>\n\n\n\n<p><strong>Answer:<\/strong> The length of one side of the box is 7 units.<\/p>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background has-medium-font-size\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-composite-numbers-from-1-to-100\/\"><strong>What are Composite Numbers from 1 to 100?<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-faqs\">FAQs<\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1723187614418\"><strong class=\"schema-faq-question\">Is 256 a perfect cube?<\/strong> <p class=\"schema-faq-answer\">No, 256 is not a perfect cube. A perfect cube is a number that can be expressed as the cube of an integer. The cube root of 256 is not an integer.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1723187621018\"><strong class=\"schema-faq-question\">Is 243 a perfect cube?<\/strong> <p class=\"schema-faq-answer\">No, 243 is not a perfect cube. A perfect cube is a number that can be expressed as the product of three identical integers. The cube root of 243 is not a whole number.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1723187643144\"><strong class=\"schema-faq-question\">Is 72 a perfect cube?<\/strong> <p class=\"schema-faq-answer\">No, 72 is not a perfect cube. A perfect cube is a number that can be expressed as the product of three identical integers. The prime factorization of 72 contains a factor of 3 that is not in groups of three, making it impossible to form a perfect cube.<\/p> <\/div> <\/div>\n\n\n\n<p>This was all about \u201c<strong>All Perfect Cube Numbers<\/strong>\u201d. For more such informative blogs, check out our<a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/study-material\/\"> Study Material Section<\/a>, or you can learn more about us by visiting our<a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/\">&nbsp; Indian exams<\/a> page.<\/p>\n","protected":false},"excerpt":{"rendered":"A perfect cube is a number that can be expressed as the product of an integer multiplied by&hellip;\n","protected":false},"author":115,"featured_media":839861,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[369,476,396],"tags":[],"class_list":{"0":"post-839851","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-indian-exams","8":"category-maths","9":"category-study-material"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.3) - 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I find peace and purpose in crafting verses that dance between the lines of poetry. With my pen as my wand, I weave intricate tales and heartfelt musings, breathing life into the blank canvas of each page. Blogging is my window to the world way of sharing thoughts, emotions, and a perspective uniquely my own. Every word I write is a brushstroke in the ever-evolving painting of my literary journey.","sameAs":["https:\/\/www.instagram.com\/xx_a.m.strings_xiv\/","https:\/\/www.linkedin.com\/in\/mohit-rajak-a9a5a2162\/"],"url":"https:\/\/leverageedu.com\/discover\/author\/mohit\/"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-all-perfect-cube-numbers\/#faq-question-1723187614418","position":1,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-all-perfect-cube-numbers\/#faq-question-1723187614418","name":"Is 256 a perfect cube?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"No, 256 is not a perfect cube. A perfect cube is a number that can be expressed as the cube of an integer. The cube root of 256 is not an integer.","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-all-perfect-cube-numbers\/#faq-question-1723187621018","position":2,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-all-perfect-cube-numbers\/#faq-question-1723187621018","name":"Is 243 a perfect cube?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"No, 243 is not a perfect cube. A perfect cube is a number that can be expressed as the product of three identical integers. The cube root of 243 is not a whole number.","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-all-perfect-cube-numbers\/#faq-question-1723187643144","position":3,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-all-perfect-cube-numbers\/#faq-question-1723187643144","name":"Is 72 a perfect cube?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"No, 72 is not a perfect cube. A perfect cube is a number that can be expressed as the product of three identical integers. The prime factorization of 72 contains a factor of 3 that is not in groups of three, making it impossible to form a perfect cube.","inLanguage":"en-US"},"inLanguage":"en-US"}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/839851","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/users\/115"}],"replies":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/comments?post=839851"}],"version-history":[{"count":0,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/839851\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media\/839861"}],"wp:attachment":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media?parent=839851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/categories?post=839851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/tags?post=839851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}