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”.
 

We can find cube roots of 56 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 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.