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473 LearnersLast updated on August 5, 2025
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.
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Grade 1
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Cube root of 108 Examples
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?
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
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