261 LearnersLast updated on May 26th, 2025
Cube Root of 56
We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 56, and its examples.
What Is the Cube Root of 56?
The cube root of 56 is the value which, when multiplied by itself three times (cubed), gives the original number 56. The cube root of 56 is 3.82586236554. The cube root of 56 is expressed as ∛56 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (56)â…“. If “m” is the cube root of 56, then, m3=56. Let us find the value of “m”.
Finding the Cubic Root of 56
We can find cube roots of 56 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cubic Root of 56 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 56.
Step 1: Let a=56. Let us take x as 3, since 33=27 is the nearest perfect cube which is less than 56.
Step 2: Apply the formula. ∛56≅ 3((33+2×56) / (2(3)3+56)) = 3.79…
Hence, 3.79… is the approximate cubic root of 56.
Common Mistakes and How to Avoid Them in the Cube Root of 56
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Mistake 1
For ∛56, students can make error in the important part of prime factorization.
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 56 Examples
Problem 1
Find (∛112/ ∛56) × (∛112/ ∛56) × (∛112/ ∛56)
(∛112/ ∛56) × (∛112/ ∛56) × (∛112/ ∛56)
= (∛112× âˆ›112× âˆ›112) / (∛56× âˆ›56× âˆ›56)
=((112)â…“)3/ ((56)â…“)3
=112/56
=2
Answer: 2
Explanation
We solved and simplified the exponent part first using the fact that, ∛112=(112)⅓ and ∛56=(56)⅓ , then solved.
Problem 2
If y = ∛56, find y3/ y6
Explanation
Problem 3
Explanation
Problem 4
Explanation
Problem 5
Explanation
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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.
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