367 LearnersLast updated on May 26th, 2025
Cube Root of 100
The cube root of 100 is the value that, when multiplied by itself three times (cubed), gives the original number 100. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, creating digital art, field of engineering, making financial decisions etc.
What Is the Cube Root of 100?
The cube root of 100 is 4.64158883361. The cube root of 100 is expressed as β100 in radical form, where the “ β ” sign is called the “radical” sign. In exponential form, it is written as (100)β . If “m” is the cube root of 100, then, m3=100. Let us find the value of “m”.
Finding the Cube Root of 100
The cube root of 100 is expressed as β100 as its simplest radical form,
since 100 = 2×2×5×5
β100 = β(2×2×5×5)
Group together three same factors at a time and put the remaining factor under the β .
β100= β100
We can find cube root of 100 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 100 By Halleyβs Method
Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N,
where this method approximates the value of “x”.
Formula is βa≅ x((x3+2a) / (2x3+a)), where
a=given number whose cube root you are going to find
x=integer guess for the cubic root
Let us apply Halley’s method on the given number 100.
Step 1: Let a=100. Let us take x as 4, since, 43=64 is the nearest perfect cube which is less than 100.
Step 2: Apply the formula. β100≅ 4((43+2×100) / (2(4)3+100))= 4.63…
Hence, 4.63… is the approximate cubic root of 100.
Common Mistakes and How to Avoid Them in the Cube Root of 100
Here are some common mistakes with their solutions given :
Mistake 1
Students might make errors during factorization. For β100, students can make error in the crucial part and may write as β100=5 3
Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair)
Cube Root of 100 Examples
Problem 1
Find (β200/ β100) Γ (β200/ β100) Γ (β200/ β100)
(β200/ β100) × (β200/ β100) × (β200/ β100)
= (β200× β200× β200) / (β100× β100× β100)
=((200)β
)3/ ((100)β
)3
=200/100
=2
Answer: 2
Explanation
We solved and simplified the exponent part first using the fact that, β200=(100)β and β100=(100)β , then solved.
Problem 2
If y = β100, find yΒ³/ yβΆ
y=β100
⇒ y3/y6= (β100)3 / (β100)6
⇒ y3/y6
= 100/ (100)2
= 1/100
Answer: 1/100
Explanation
(β100)3=(1001/3)3=100, and β100)6=(1001/3)6=(16)2. Using this, we found the value of y3/y6.
Problem 3
Multiply β100 Γ β125
β100×β125
= 4.641×5
=23.205
Answer: 23.205
Explanation
We know that the cubic root of 125 is 5, hence multiplying β125 with β100.
Problem 4
What is β(100βΆ) ?
β(1006)
= ((100)6))1/3
=( 100)2
= 10000
Answer: 10000
Explanation
We solved and simplified the exponent part first using the fact that, β100=(100)β
, then solved.
Problem 5
Find β(100+(-36)).
β(100-36)
= β64
=4
Answer: 4
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 100 Cube Root
1.What are the perfect cubes less than 100?
2.Is 14 a perfect square ?
3.What is the cube root of 8?
4.Is 100 a cube number?
5.How to solve β1000 ?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube Root of 100?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube Root of 100?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube Root of 100
- Integers: Integers can be a positive natural number, a 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.
- Polynomial: It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole-number exponents.
- Approximation: Finding out a value that is nearly correct, but not perfectly correct.
- Iterative method : This method is a mathematical process that uses an initial value to generate a further and step-by-step sequence of solutions for a problem.
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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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