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592 LearnersLast updated on August 5, 2025
Cube Root of 75
What Is the Cube Root of 75 ?
The cube root of 75 is 4.21716332651. The cube root of 75 is expressed as ∛75 in radical form, where the “∛" sign is called the “radical” sign. In exponential form, it is written as (75)⅓. If “m” is the cube root of 75, then, m3=75. Let us find the value of “m”.
Finding the Cube Root of 75
The cube root of 75 is expressed as ∛75 as its simplest radical form,
since 75 = 5×5×3
∛75 = ∛(5×5×3)
Group together three same factors at a time and put the remaining factor under the ∛ .
∛75= ∛75
We can find cube root of 75 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 75 By Halley’s 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 ∛a≅ 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 75.
Step 1: Let a=75. Let us take x as 4, since, 43=64 is the nearest perfect cube which is less than 75.
Step 2: Apply the formula. ∛75≅ 4((43+2×75) / (2(4)3+75))= 4.12…
Hence, 4.12… is the approximate cubic root of 75.
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Common Mistakes and How to Avoid Them in the Cube Root of 75
Here are some common mistakes with their solutions given:
Mistake 1
Students might guess the cube root by rounding to the nearest number, leading to inaccuracy. For ∛125, the student might mistakenly think the answer is 4, where 53 is the correct answer.
Don’t round off to the nearest number and find cube roots,It is advisable to use proper methods to find cube roots.
Mistake 2
Students forget the concept of cube roots often, by not understanding the definition.
This happens because of uncleared understanding of cube roots and the methods to find it.
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.
Mistake 4
Students often rely on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complex problems. So understanding the methods of finding cube roots is advisable.
Mistake 5
Not checking for perfect cubes, like that of 27, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 100.
Cube Root of 75 Examples
Problem 1
Find (∛75/ ∛64) × (∛75/ ∛64) × (∛75/ ∛64)
(∛75/ ∛64) × (∛75/ ∛64) × (∛75/ ∛64)
= (∛75× ∛75× ∛75) / (∛64× ∛64× ∛64)
=((75)⅓)3/ ((64)⅓)3
=75/64
Answer: 75/64
Explanation
We solved and simplified the exponent part first using the fact that, ∛75=(75)⅓ and ∛64=(64)⅓ , then solved.
Problem 2
If y = ∛75, find y³.
y=∛75
⇒ y3= (∛75)3
⇒ y3= 75
Answer: 75
Explanation
(∛75)3=(751/3)3=75. Using this, we found the value of y3.
Problem 3
Subtract ∛75 - ∛64
∛75-∛64
= 4.217–4
= 0.217
Answer: 0.217
Explanation
We know that the cubic root of 64 is 4, hence subtracting ∛64 from ∛75.
Problem 4
What is ∛(75⁶) ?
∛(756)
= ((75)6))1/3
=( 75)2
= 5625
Answer: 5625
Explanation
We solved and simplified the exponent part first using the fact that, ∛75=(75)⅓, then solved.
Problem 5
Find ∛(75+(-11)).
∛(75-11)
= ∛64
= 4
Answer: 4
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 75 Cube Root
1.∛75 lies between which two perfect cubes?
2.Is 75 a perfect cube?
3.What is the simplified form of ∛75?
4.What is the square root of 75?
5.How to find a cube root without using a calculator?
Important Glossaries for Cube Root of 75
- 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.
- 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 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.
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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.
