Cube root of 108
2026-02-28 08:52 Diff
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Last updated on August 5, 2025

Having an understanding of the concept of cube root is essential in the fields of engineering, construction and science. Cube roots are also used to measure volumes in three-dimensional spaces on a daily basis. Let us now learn about the cube root of 108.

What is the cube root of 108?

∛108 = 4.762203. 


We can arrive at the cube root of a given number using; 

  • Halley’s method — Use of approximation to find the cube root 
  • Prime factorization — we break 108 into its prime factors to find the cube root 
  • Estimation method — we analyze the given number between two known perfect cubes. Let us now learn in detail; 

Cube root of 108 by Halley’s method

Halley’s method is a proven effective method for finding the cube root of a number. We use the below formula; 


∛a≅ x((x3+2a) / (2x3+a))


In the formula; 


a = given number, 108 


x = integer guess for the cube root, i.e., a number close to the cube root of 108


Steps to find the cube root:


a = 108, for approximation choose, x = 4, it is the nearest cube (43=64).

 
Now apply the formula; 


∛a≅ x((x3+2a) / (2x3+a))


∛108≅ 4((43+2.108) / (2.43+108)) = 4.76 


The approximate cube of 108 = 4.76
 

Common mistakes and how to avoid them in cube root of 108

While solving ∛108, few mistakes are common in children’s worksheet. To avoid those mistakes, few solutions are given below - 
 

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Problem 1

(∛108+∛108)×∛108, simplify.

Okay, lets begin

(∛108+∛108)×∛108

= (4.762+4.762)×4.762

= 9.524×4.762

= 45.37
 

Explanation

The simplified value is 45.37. 
 

Well explained 👍

Problem 2

If x= ∛108, find x²-x.

Okay, lets begin

x = 4.762


x2 = 22.68


x2 −x = 22.68−4.762

= 17.92
 

Explanation

 x2-x is 17.92. 
 

Well explained 👍

Problem 3

Multiply ∛108 and ∛216

Okay, lets begin

∛108×∛216

= 4.762×6

= 28.57 
 

Explanation

multiplying value of cube root of 108 and 216 togather.

Well explained 👍

FAQs on the cube root of 108

1.What is the cube of 108?

2.Simplify root 108.

3.Is 108 a perfect square?

4.What are the factors of 108?

1,2,3,4,6,9,12,18,27,36,54 and 108. 
 

5.How do you make 108 a perfect cube ?

You can make 108 a perfect cube by just adding 17. 108+17 =125, 125 is a perfect cube. 
 

Important Glossaries for Cube root of 108

  • 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. 

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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.