Cube Root of 128
2026-02-28 19:09 Diff
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Last updated on August 5, 2025

The cube root of 128 is the value that, when multiplied by itself three times (cubed), gives the original number 128. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.

What Is the Cube Root of 128?

The cube root of 128 is 5.03968419958. The cube root of 128 is expressed as ∛128 in radical form, where the “∛"  sign is called the “radical” sign.

In exponential form, it is written as (128)⅓. If “m” is the cube root of 128, then, m3=128. Let us find the value of “m”.
 

Finding the Cube Root of 128

The cube root of 128 is expressed as 4∛2 as its simplest radical form,

since 128 = 2×2×2×2×2×2×2


∛128 = ∛(2×2×2×2×2×2×2)


Group together three same factors at a time and put the remaining factor under the ∛ .


∛128= 4∛2 


 We can find cube root of 128 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 128 By Halley’s Method

Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.


Formula is ∛a≅ x((x3+2a) / (2x3+a)), where 


a=given number whose cube root you are going to find.


x=integer guess for the cubic root


 Let us apply Halley’s method on the given number 128.


Step 1: Let a=128. Let us take x as 5, since, 53=125 is the nearest perfect cube which is less than 128.


Step 2: Apply the formula.  ∛128≅ 5((53+2×128) / (2(5)3+128))= 5.039…


Hence, 5.039… is the approximate cubic root of 128.
 

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Common Mistakes and How to Avoid Them in the Cubic Root of 128

some common mistakes and their solutions are given below:

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Problem 1

Find (∛128/ ∛64) × (∛128/ ∛64) × (∛128/ ∛64)

Okay, lets begin

 (∛128/ ∛64) × (∛128/ ∛64) × (∛128/ ∛64)


= (∛128× ∛128× ∛128) / (∛64× ∛64× ∛64)


=((128)⅓)3/ ((64)⅓)3


=128/64


= 2


Answer:       2
 

Explanation

We solved and simplified the exponent part first using the fact that, ∛128=(128)⅓ and ∛64=(64)⅓ , then solved.
 

Well explained 👍

Problem 2

If y = ∛128, find y^3.

Okay, lets begin

 y=∛128


⇒ y3= (∛128)3 


⇒ y3= 128


Answer:     128
 

Explanation

 (∛128)3=(1281/3)3=128.

Using this, we found the value of y3.
 

Well explained 👍

Problem 3

Subtract ∛128 - ∛125

Okay, lets begin

 ∛128-∛125

= 5.039–5

= 0.039


Answer:      0.039
 

Explanation

We know that the cubic root of 125 is 5, hence subtracting  ∛125 from ∛128.
 

Well explained 👍

Problem 4

What is ∛(128^6) ) ?

Okay, lets begin

 ∛(1286)

= ((128)6))1/3

=( 128)2

= 16384

Answer:     16384

Explanation

We solved and simplified the exponent part first using the fact that, ∛128=(128)⅓, then solved.
 

Well explained 👍

Problem 5

Find ∛(128+(-3))

Okay, lets begin

 ∛(128-3)

= ∛125

= 5


Answer:      5
 

Explanation

Simplified the expression, and found out the cubic root of the result. 
 

Well explained 👍

FAQs on 128 Cube Root

1.∛128 lies between which two perfect cubes?

∛128=5.03… lies between perfect cubes 1 and 8.

2.What are the factors of 128?

 The factors of 128 are 1,2,4,8,16,32,64 and 128. 

3.What is the simplest form of ∛108?

108 = 2×2×3×3×3


∛108 = ∛(2×2×3×3×3)


∛108= 3∛4


3∛4 is the simplest radical form of 108 
 

4.Is 108 a perfect cube?

 No, 108 is not a perfect cube.
 

5.Is 72 a perfect square?

Important Glossaries for Cubic Root of 128

  • Integers:  Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.
  • Whole numbers: The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. 
  • Square root: The square root of a number is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is the original number.
  • Polynomial: It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
  • Approximation:  Finding out a value which is nearly correct, but not perfectly correct.
  • Iterative method: This method is a mathematical process which uses an initial value to generate further and step-by-step sequence of solutions for a problem.

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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.

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