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”.
 

We can find cube roots of 120 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 ∛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.