Table Of Contents
247 LearnersLast updated on January 10th, 2025
Cube Root of 128
The cube root of 128 is the value that, when multiplied by itself three times (cubed), gives the original number 128. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.
What Is the Cube Root of 128?
The cube root of 128 is 5.03968419958. The cube root of 128 is expressed as β128 in radical form, where the ββ" sign is called the βradicalβ sign.
In exponential form, it is written as (128)β
. If βmβ is the cube root of 128, then, m3=128. Let us find the value of βmβ.
Finding the Cube Root of 128
The cube root of 128 is expressed as 4β2 as its simplest radical form,
since 128 = 2Γ2Γ2Γ2Γ2Γ2Γ2
β128 = β(2Γ2Γ2Γ2Γ2Γ2Γ2)
Group together three same factors at a time and put the remaining factor under the β .
β128= 4β2
We can find cube root of 128 through a method, named as, Halleyβs Method. Let us see how it finds the result.
Cube Root of 128 By Halleyβs Method
Now, what is Halleyβs 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 βxβ.
Formula is βaβ
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 Halleyβs method on the given number 128.
Step 1: Let a=128. Let us take x as 5, since, 53=125 is the nearest perfect cube which is less than 128.
Step 2: Apply the formula. β128β
5((53+2Γ128) / (2(5)3+128))= 5.039β¦
Hence, 5.039β¦ is the approximate cubic root of 128.
Common Mistakes and How to Avoid Them in the Cubic Root of 128
some common mistakes and their solutions are given below:
Mistake 3
For large non-perfect cubes, students often estimate wrongly and leave it with a wrong result.
Keep the methods of finding cube roots in front whenever attempting large non-perfect cubes.
Cube Root of 128 Examples
Problem 1
Find (β128/ β64) Γ (β128/ β64) Γ (β128/ β64)
(β128/ β64) Γ (β128/ β64) Γ (β128/ β64)
= (β128Γ β128Γ β128) / (β64Γ β64Γ β64)
=((128)β
)3/ ((64)β
)3
=128/64
= 2
Answer: 2
Explanation
We solved and simplified the exponent part first using the fact that, β128=(128)β
and β64=(64)β
, then solved.
Problem 2
If y = β128, find y^3.
y=β128
β y3= (β128)3
β y3= 128
Answer: 128
Explanation
(β128)3=(1281/3)3=128.
Using this, we found the value of y3.
Problem 3
Subtract β128 - β125
β128-β125
= 5.039β5
= 0.039
Answer: 0.039
Explanation
We know that the cubic root of 125 is 5, hence subtracting β125 from β128.
Problem 4
What is β(128^6) ) ?
β(1286)
= ((128)6))1/3
=( 128)2
= 16384
Answer: 16384
Explanation
We solved and simplified the exponent part first using the fact that, β128=(128)β
, then solved.
Problem 5
Find β(128+(-3))
β(128-3)
= β125
= 5
Answer: 5
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 128 Cube Root
1.β128 lies between which two perfect cubes?
2.What are the factors of 128?
3.What is the simplest form of β108?
4.Is 108 a perfect cube?
5.Is 72 a perfect square?
Important Glossaries for Cubic Root of 128
- 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 βyβ such that when βyβ is multiplied by itself β y ‫ y, the result is the original number.
- Polynomial: It is an algebraic expression made up of variables like βxβ and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
- Approximation: Finding out a value which is nearly correct, but not perfectly correct.
- Iterative method: This method is a mathematical process which uses an initial value to generate further and step-by-step sequence of solutions for a problem.
Explore More algebra
Previous to Cube Root of 128
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.
