Last updated on May 26th, 2025
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.
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”.
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.
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.
here are some common mistakes with their solutions are given:
Find β54 / 3779.
(β54) / 3779
= 3.779 /3779
= 0.001
Answer: 0.001
Simplified the expression, and found out the result.
Find β(54-(-10)).
β(54-(-10))
= β54+10
= β64
= 4
Answer: 4
Simplified the expression, and found out the cubic root of the result.
What is β(54^6) ?
β(546)
= ((54)6))1/3
=( 54)2
= 2916
Answer: 2916
We solved and simplified the exponent part first using the fact that, β54=(54)β
, then solved.
Multiply β54 Γ β64 Γ β125
β54×β64× β125
= 3.779×4×5
= 75.58
Answer: 75.58
We know that the cubic root of 64 is 4 and that of 125 is 5, hence multiplying.
Find β(16+(-8)+24+(-7)+2).
β(16-8+24-7+2)
= β27
=3
Answer: 3
Simplified the expression, and found out the cubic root of the result.
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.
: He loves to play the quiz with kids through algebra to make kids love it.