278 LearnersLast updated on May 26th, 2025
Cube root of 108
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 -
Mistake 1
Confusing cube roots with square roots
Sometimes one may think ∛108 and √108 are the same, leading to unnecessary calculations.
Mistake 2
Faulty application of exponent rules
While practicing, one may get confused between the cube root (∛a) of a number and cubing a number (a3), be mindful.
Mistake 3
Rounding too early
Do not round off when intermediate results are achieved, if the calculation is not complete.
Cube root of 108 Examples
Problem 1
(∛108+∛108)×∛108, simplify.
(∛108+∛108)×∛108
= (4.762+4.762)×4.762
= 9.524×4.762
= 45.37
Explanation
The simplified value is 45.37.
Problem 2
If x= ∛108, find x²-x.
x = 4.762
x2 = 22.68
x2 −x = 22.68−4.762
= 17.92
Explanation
x2-x is 17.92.
Problem 3
Multiply ∛108 and ∛216
∛108×∛216
= 4.762×6
= 28.57
Explanation
multiplying value of cube root of 108 and 216 togather.
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?
5.How do you make 108 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.
