Cube Root of 48

The cube root of 48 is the value which, when multiplied by itself three times (cubed), gives the original number 48. The cube root of 48 is 3.63424118566.  In exponential form, it is written as (48)^⅓. If “m” is the cube root of 48, then, m³=48. Let us find the value of “m”.
 

We can find cube root of 48 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 48.

Step 1: Let a=48. Let us take x as 3, since, 3³=27 is the nearest perfect cube which is less than 48.

Step 2: Apply the formula.  ∛48≅ 3((3³+2×48) / (2(3)³+48))= 3.62…

Hence, 3.62… is the approximate cubic root of 48
 

• Irrational Numbers - All numbers cannot be expressed as p/q, where p and q are integers and q not equal to 0. Those numbers are called Irrational numbers.

• Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. 

• Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be taken out.

• Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.

• Approximation - Finding out a value which is nearly correct, but not perfectly correct.

• Iterative method - This method is a mathematical process which uses an initial value to generate further and step-by-step sequence of solutions for a problem.