Cube root of 64
2026-02-28 13:46 Diff
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Last updated on August 5, 2025

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.

What is the cube root of 64?

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

Finding the cube root of 64

We can find the cube root of 64, mainly through two methods: 


i) Prime Factorization method.


ii) Subtraction method.
 

Cube root of 64 by Prime Factorization method

Finding a cube root of 64 through the Prime Factorization method involves determining the factor of 64.


Step 1 — Find the prime factors of 64. 

So, 64 = 2×2×2×2×2×2


Step 2 — Group the factors of 64 together in a group of 3(i.e., power of 3).


Step 3 — Here, we get two triplet groups of factor 2 in the power of 3, i.e., 23 or 2×2×2 

The cube root of 64 can be written as ∛64 = ∛(2×2×2)×(2×2×2) = 2×2 = 4 


Therefore, the cube root of 64 is 4.

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Cube root of 64 by Subtraction method

This method involves subtracting successive odd numbers repeatedly. The list of odd numbers that should be subtracted successively are →

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

Step 1 — Subtract the 1st odd number : 64–1 = 63 


Step 2 — Subtract the next odd number: 63–7 = 56


Step 3 — Subtract the next odd number: 56–19 = 37


Step 4 — Subtract the next odd number: 37–37 = 00


Here, the subtraction took place four times to reach zero.


Hence, the cube root of 64 is 4. 
 

Common Mistakes and How to Avoid Them in the Cubic Root of 64

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.

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Problem 1

Is 64 a perfect cube?

Okay, lets begin

Answer:   Yes
 

Explanation

 64 can be expressed as 4×4×4, hence it is a perfect cube. 
 

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Problem 2

If the volume of a cube is 64 cubic units, what is the length of each side?

Okay, lets begin

Answer:    4
 

Explanation

Volume of Cube = a3, Where a is the side length


Since,  a3 = 64, a = ∛64


Hence, a = 4
 

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Problem 3

Solve the equation (X³ = 64)

Okay, lets begin

 (X3 = 64)


X = ∛64


X = 4 
 

Explanation

Solving the equation, and found the value of x.
 

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Problem 4

Multiply ∛64 × ∛125

Okay, lets begin

 ∛64×∛125

= 4×5

= 20


Answer: 20
 

Explanation

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

Well explained 👍

FAQs on 64 Cube root

1.What is the value of 3∛ 64

2.Is 12 a cube root?

3.Is √12 irrational

4.Is cube root a real number

Important Glossaries for Cube Root of 64

  • Cubic root —  The number when multiplied with itself 3 times gives the original number is called as Cubic root.
  • Prime Factorization — Find out prime factors for given number.
  • Exponent — The number to which the power is raised. In (64)⅓, ⅓ is the exponent.
  • Irrational number – A number that does not follow the definition of rational.
     

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Jaskaran Singh Saluja

About the Author

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.