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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The cube root of 216 is the value “y” such that the number “y” is multiplied thrice by itself. ∛ is the symbol used to denote the cube root of a number. Cube roots are used in designing loudspeakers or in pharmacology for correct dosage of medicine as per body weight.</p>

4 <h2>What Is the Cube Root of 216 ?</h2>

5 <p>The<a>cube</a>root of 216 is<strong>6</strong>. The cube root of 216 is expressed as ∛216 in radical form, where the “∛" sign is called the “radical” sign. In<a>exponential form</a>, it is written as (216)⅓ </p>

6 <h2>Finding the Cube Root of 216</h2>

7 <p>We can find the<a>cube root</a>of 216, mainly through two methods: </p>

8 <ul><li>Prime Factorization method.</li>

9 </ul><ul><li>Subtraction method </li>

10 </ul><h3>Cubic Root of 216 By Prime Factorization</h3>

11 <p>Finding a cube root of 216 through the Prime Factorization method involves determining the<a>factor</a>of 216.</p>

12 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of 216. So 216 = 2×2×2×3×3×3</p>

13 <p><strong>Step 2:</strong>Group the factors of 216 in a group of 3.</p>

14 <p><strong>Step 3:</strong>Since 216 is a<a>perfect cube</a>, we have two pairs of 3 digits.</p>

15 <p>The cube root of 216 can be written as ∛216 = ∛(2×2×2)×(3×3×3) = 2×3 = 6 </p>

16 <p>Therefore, the cube root of 216 is<strong>6</strong>. </p>

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19 <h3>Cube Root of 216 By Subtraction Method</h3>

18 <h3>Cube Root of 216 By Subtraction Method</h3>

20 <p>The<a>subtraction</a>method involves subtracting successive<a>odd numbers</a>repeatedly. </p>

19 <p>The<a>subtraction</a>method involves subtracting successive<a>odd numbers</a>repeatedly. </p>

21 <p>Subtract the numbers 1,7,19,37,61,91,127,169,217,331,397……..successively till we get a zero. </p>

20 <p>Subtract the numbers 1,7,19,37,61,91,127,169,217,331,397……..successively till we get a zero. </p>

22 <p><strong>Step 1:</strong>Subtract the 1st odd number : 216-1 = 215 </p>

21 <p><strong>Step 1:</strong>Subtract the 1st odd number : 216-1 = 215 </p>

23 <p><strong>Step 2:</strong>Subtract the next odd number: 215-7 = 208</p>

22 <p><strong>Step 2:</strong>Subtract the next odd number: 215-7 = 208</p>

24 <p><strong>Step 3:</strong>Subtract the next odd number: 208-19 = 189</p>

23 <p><strong>Step 3:</strong>Subtract the next odd number: 208-19 = 189</p>

25 <p><strong>Step 4:</strong>Subtract the next odd number: 189-37 = 152</p>

24 <p><strong>Step 4:</strong>Subtract the next odd number: 189-37 = 152</p>

26 <p><strong>Step 5:</strong>Subtract the next odd number: 152-61 = 91</p>

25 <p><strong>Step 5:</strong>Subtract the next odd number: 152-61 = 91</p>

27 <p><strong>Step 6:</strong>Subtract the next odd number: 91 - 91 = 0</p>

26 <p><strong>Step 6:</strong>Subtract the next odd number: 91 - 91 = 0</p>

28 <p>Here, the subtraction took place six times to reach zero.</p>

27 <p>Here, the subtraction took place six times to reach zero.</p>

29 <p>Hence, the cube root of 216 is 6. </p>

28 <p>Hence, the cube root of 216 is 6. </p>

30 <p><strong>216-1 = 215</strong></p>

29 <p><strong>216-1 = 215</strong></p>

31 <p><strong>215-7= 208</strong></p>

30 <p><strong>215-7= 208</strong></p>

32 <p><strong>208-19=189</strong></p>

31 <p><strong>208-19=189</strong></p>

33 <p><strong>189-37=152</strong></p>

32 <p><strong>189-37=152</strong></p>

34 <p><strong>152-61=91</strong></p>

33 <p><strong>152-61=91</strong></p>

35 <p><strong>91-91=0 </strong></p>

34 <p><strong>91-91=0 </strong></p>

36 <h2>Common Mistakes and How to Avoid Them in Cube Root of 216</h2>

35 <h2>Common Mistakes and How to Avoid Them in Cube Root of 216</h2>

37 <p>While finding the cube root of 216, there are some common mistakes that we often make. So let’s discuss a few of the mistakes and their solutions. </p>

36 <p>While finding the cube root of 216, there are some common mistakes that we often make. So let’s discuss a few of the mistakes and their solutions. </p>

37 + <h2>Download Worksheets</h2>

38 <h3>Problem 1</h3>

39 <p>Given the volume of a cube is 216 cubic inches, find the length of one side of the cube.</p>

40 <p>Okay, lets begin</p>

41 <p>6 inches. </p>

42 <h3>Explanation</h3>

43 <p> Volume of cube = a3, where a is the side length</p>

44 <p>Equation: a3= 216 </p>

45 <p>Apply the cube root: a = ∛216</p>

46 <p>Simplify:</p>

47 <p>a = ∛2×2×2×3×3×3</p>

48 <p>= 2×3</p>

49 <p>= 6 </p>

50 <p>Well explained 👍</p>

51 <h3>Problem 2</h3>

52 <p>Express the cube root of 216 in exponential form.</p>

53 <p>Okay, lets begin</p>

54 <p>(216)⅓ </p>

55 <h3>Explanation</h3>

56 <p>The cube root of any number can be expressed as (a)⅓ </p>

57 <p>Well explained 👍</p>

58 <h3>Problem 3</h3>

59 <p>Find the cube root of 216 by estimation method.</p>

60 <p>Okay, lets begin</p>

61 <p> 6 </p>

62 <h3>Explanation</h3>

63 <p> Find nearby perfect cubes: 53 = 125 and 63 = 216, Since 216 is exactly 63, the cube root is 6. </p>

64 <p>Well explained 👍</p>

65 <h2>Conclusion</h2>

66 <p>We get a cube root of a<a>number</a>when multiplied by itself three times. Methods like Prime Factorization, and subtraction methods are useful in finding the cube root of a perfect cube. Since we have found the cube root of 216 using both these methods, it has become quite simple to find the cube roots of any other number. </p>

67 <h2>FAQs on 216 cube root</h2>

68 <h3>1.How to solve the ∛225 ?</h3>

69 <p>By prime factorization method:</p>

70 <p> 225 = ∛3×3×5×5</p>

71 <p>= 6.0822 </p>

72 <h3>2.Is 0 a cube number ?</h3>

73 <h3>3.Is 27 a multiple of 9 ?</h3>

74 <h3>4.Is Pi (π) a real number ?</h3>

75 <h3>5.Can the cube root of 216 be negative?</h3>

76 <p>The cube root of 216 is 6 but if we consider the cube root of a<a>negative number</a>then the cube root would be negative. </p>

77 <h3>6.What is the relationship between the cube root of 216 and the square root of 216 ?</h3>

78 <p> There is no relationship between the cube root of 216 and the<a>square</a>root of 216. </p>

79 <h2>Important Glossaries for Cube Root of 216</h2>

80 <ul><li><strong>Exponent :</strong>It is the number that indicates how many times a base is multiplied by itself</li>

81 </ul><ul><li><strong>Radicand:</strong>It is the number that indicates how many times a base is multiplied by itself. </li>

82 </ul><ul><li><strong>Radical symbol:</strong>It is the symbol used to denote roots of numbers.</li>

83 </ul><ul><li><strong>Volume of cube:</strong>It is the amount of space occupied by a cube. </li>

84 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

85 <p>▶</p>

86 <h2>Jaskaran Singh Saluja</h2>

87 <h3>About the Author</h3>

88 <p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>

89 <h3>Fun Fact</h3>

90 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>