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; 

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
 

• 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.