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476 LearnersLast updated on August 5, 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)⅓. 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.
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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.
Mistake 2
Applying exponent rules incorrectly when finding cube roots.
∛56 is not same as 563. ∛56 = 3.82… and 563 is something very large quantity.
Mistake 3
For large non-perfect cubes, students frequently 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 typically 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
Misapply the cube root property like when asked to solve ∛(56)3, students might do as ∛(56×3)
Clear the concepts again and again if they don’t understand, where to do what. ∛(56)3≠∛(56×3). ∛(56)3= 56
Cube Root of 56 Examples
Problem 1
Find (∛112/ ∛56) × (∛112/ ∛56) × (∛112/ ∛56)
(∛112/ ∛56) × (∛112/ ∛56) × (∛112/ ∛56)
= (∛112× ∛112× ∛112) / (∛56× ∛56× ∛56)
=((112)⅓)3/ ((56)⅓)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
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.
