373 LearnersLast updated on May 26th, 2025
Cube Root of 54
The cube root of 54 is the value that, when multiplied by itself three times (cubed), gives the original number 54. 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 Cubic Root of 54?
The cube root of 54 is 3.77976314968. The cube root of 54 is expressed as β54 in radical form, where the “ β “ sign is called the “radical” sign. In exponential form, it is written as (54)β
. If “m” is the cube root of 54, then, m3=54. Let us find the value of “m”.
Finding the Cube Root of 54
The cube root of 54 is expressed as 3β2 as its simplest radical form,
since 54 = 3×3×3×2
β54 = β(3×3×3×2)
Group together three same factors at a time and put the remaining factor under the β .
β54= 3β2
We can find cube root of 54 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 54 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 54.
Step 1: Let a=54. Let us take x as 3, since, 33=27 is the nearest perfect cube which is less than 54.
Step 2: Apply the formula. β54≅ 3((33+2×54) / (2(3)3+54))= 3.75
Hence, 3.75 is the approximate cubic root of 54.
Common Mistakes and How to Avoid Them in the Cube Root of 54
here are some common mistakes with their solutions are given:
Mistake 1
Students might make errors during factorization. For β54, students can make error in the crucial part and write β54= 23
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 54 Examples
Problem 1
Find β54 / 3779.
(β54) / 3779
= 3.779 /3779
= 0.001
Answer: 0.001
Explanation
Simplified the expression, and found out the result.
Problem 2
Find β(54-(-10)).
β(54-(-10))
= β54+10
= β64
= 4
Answer: 4
Explanation
Simplified the expression, and found out the cubic root of the result.
Problem 3
What is β(54^6) ?
β(546)
= ((54)6))1/3
=( 54)2
= 2916
Answer: 2916
Explanation
We solved and simplified the exponent part first using the fact that, β54=(54)β
, then solved.
Problem 4
Multiply β54 Γ β64 Γ β125
β54×β64× β125
= 3.779×4×5
= 75.58
Answer: 75.58
Explanation
We know that the cubic root of 64 is 4 and that of 125 is 5, hence multiplying.
Problem 5
Find β(16+(-8)+24+(-7)+2).
β(16-8+24-7+2)
= β27
=3
Answer: 3
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 54 Cube Root
1.What is 3β54 simplified?
2.What is the cube of 54?
3.What is the perfect cube near 54?
4.What is cube formula?
5.How do You calculate a cube?
Important Glossaries for Cube Root of 54
- 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.
