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

3 <p>The cube root of 64 is the value “y” such that the number “y” is multiplied thrice by Itself to get the result as 64. Real life applications of cube roots are in the field of engineering, measuring density and volumes, designing structures, etc.</p>

4 <h2>What is the cube root of 64?</h2>

5 <p>The<a>cube</a>root<a>of</a>64 is 4. The cube root of 64 is expressed as ∛64 in radical form, where the “∛" sign is called the “radical” sign. In<a>exponential form</a>, it is written as (64)⅓ </p>

6 <h2>Finding the cube root of 64</h2>

7 <p>We can find the<a>cube root</a>of 64, mainly through two methods: </p>

8 <p><a>i</a>) Prime Factorization method.</p>

9 <p>ii) Subtraction method. </p>

10 <h3>Cube root of 64 by Prime Factorization method</h3>

11 <p>Finding a cube root of 64 through the Prime Factorization method involves determining the<a>factor</a>of 64.</p>

12 <p><strong>Step 1 -</strong>Find the<a>prime factors</a>of 64. </p>

13 <p>So, 64 = 2×2×2×2×2×2</p>

14 <p><strong>Step 2 -</strong>Group the factors of 64 together in a group of 3(i.e.,<a>power</a>of 3).</p>

15 <p><strong>Step 3 -</strong>Here, we get two triplet groups of factor 2 in the power of 3, i.e., 23 or 2×2×2 </p>

16 <p>The cube root of 64 can be written as ∛64 = ∛(2×2×2)×(2×2×2) = 2×2 = 4 </p>

17 <p>Therefore, the cube root of 64 is 4.</p>

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20 <h3>Cube root of 64 by Subtraction method</h3>

19 <h3>Cube root of 64 by Subtraction method</h3>

21 <p>This method involves subtracting successive<a>odd numbers</a>repeatedly. The<a>list of odd numbers</a>that should be subtracted successively are →</p>

20 <p>This method involves subtracting successive<a>odd numbers</a>repeatedly. The<a>list of odd numbers</a>that should be subtracted successively are →</p>

22 <p>1,7,19,37,61,91,127,169,217,331,397 … This iteration will continue till we get a zero. </p>

21 <p>1,7,19,37,61,91,127,169,217,331,397 … This iteration will continue till we get a zero. </p>

23 <p><strong>Step 1 -</strong>Subtract the 1st odd number : 64-1 = 63 </p>

22 <p><strong>Step 1 -</strong>Subtract the 1st odd number : 64-1 = 63 </p>

24 <p><strong>Step 2 -</strong>Subtract the next odd number: 63-7 = 56</p>

23 <p><strong>Step 2 -</strong>Subtract the next odd number: 63-7 = 56</p>

25 <p><strong>Step 3 -</strong>Subtract the next odd number: 56-19 = 37</p>

24 <p><strong>Step 3 -</strong>Subtract the next odd number: 56-19 = 37</p>

26 <p><strong>Step 4 -</strong>Subtract the next odd number: 37-37 = 00</p>

25 <p><strong>Step 4 -</strong>Subtract the next odd number: 37-37 = 00</p>

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

26 <p>Here, the<a>subtraction</a>took place four times to reach zero.</p>

28 <p>Hence, the cube root of 64 is 4. </p>

27 <p>Hence, the cube root of 64 is 4. </p>

29 <h2>Common Mistakes and How to Avoid Them in the Cubic Root of 64</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Cubic Root of 64</h2>

30 <p>While finding the cube root of 64, we often need to correct some common mistakes. So let’s discuss a few of the errors and their solutions.</p>

29 <p>While finding the cube root of 64, we often need to correct some common mistakes. So let’s discuss a few of the errors and their solutions.</p>

30 + <h2>Download Worksheets</h2>

31 <h3>Problem 1</h3>

32 <p>Is 64 a perfect cube?</p>

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

34 <p>Answer: Yes </p>

35 <h3>Explanation</h3>

36 <p> 64 can be expressed as 4×4×4, hence it is a perfect cube. </p>

37 <p>Well explained 👍</p>

38 <h3>Problem 2</h3>

39 <p>If the volume of a cube is 64 cubic units, what is the length of each side?</p>

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

41 <p>Answer: 4 </p>

42 <h3>Explanation</h3>

43 <p>Volume of Cube = a3, Where a is the side length</p>

44 <p>Since, a3 = 64, a = ∛64</p>

45 <p>Hence, a = 4 </p>

46 <p>Well explained 👍</p>

47 <h3>Problem 3</h3>

48 <p>Solve the equation (X³ = 64)</p>

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

50 <p> (X3 = 64)</p>

51 <p>X = ∛64</p>

52 <p>X = 4 </p>

53 <h3>Explanation</h3>

54 <p>Solving the equation, and found the value of x. </p>

55 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

57 <p>Multiply ∛64 × ∛125</p>

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

59 <p> ∛64×∛125</p>

60 <p>= 4×5</p>

61 <p>= 20</p>

62 <p>Answer: 20 </p>

63 <h3>Explanation</h3>

64 <p>We know that the cubic root of 125 is 5, hence multiplying ∛125 with ∛64. </p>

65 <p>Well explained 👍</p>

66 <h2>FAQs on 64 Cube root</h2>

67 <h3>1.What is the value of 3∛ 64</h3>

68 <h3>2.Is 12 a cube root?</h3>

69 <h3>3.Is √12 irrational</h3>

70 <h3>4.Is cube root a real number</h3>

71 <h2>Important Glossaries for Cube Root of 64</h2>

72 <ul><li><strong>Cubic root -</strong> The number when multiplied with itself 3 times gives the original number is called as Cubic root.</li>

73 </ul><ul><li><strong>Prime Factorization -</strong>Find out prime factors for given number.</li>

74 </ul><ul><li><strong>Exponent -</strong>The number to which the power is raised. In (64)⅓, ⅓ is the exponent.</li>

75 </ul><ul><li><strong>Irrational number -</strong>A number that does not follow the definition of rational. </li>

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

77 <p>▶</p>

78 <h2>Jaskaran Singh Saluja</h2>

79 <h3>About the Author</h3>

80 <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>

81 <h3>Fun Fact</h3>

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