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Last updated on November 30th, 2024

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Cube root of 108

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Foundation
Intermediate
Advance Topics

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.

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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; 
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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
 

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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.