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105 LearnersLast updated on November 30th, 2024
Cube Root of 120
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 120, and its examples
What Is the Cube Root of 120?
The cube root of 120 is the value which, when multiplied by itself three times (cubed), gives the original number 120. The cube root of 120 is 4.93242414866. The cube root of 120 is expressed as ∛120 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (120)⅓. If “m” is the cube root of 120, then, m3=120. Let us find the value of “m”.
Finding the Cubic Root of 120
We can find cube roots of 120 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 120 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 120.
Step 1: Let a=120. Let us take x as 4, since 43=64 is the nearest perfect cube which is less than 120.
Step 2: Apply the formula. ∛120≅ 4((43+2×120) / (2(4)3+120)) = 4.9…
Hence, 4.9… is the approximate cubic root of 120.
