Cube Root of 128

The cube root of 128 is 5.03968419958. The cube root of 128 is expressed as ∛128 in radical form, where the “∛"  sign is called the “radical” sign.

In exponential form, it is written as (128)^⅓. If “m” is the cube root of 128, then, m³=128. Let us find the value of “m”.
  

The cube root of 128 is expressed as 4∛2 as its simplest radical form,

since 128 = 2×2×2×2×2×2×2

∛128 = ∛(2×2×2×2×2×2×2)

Group together three same factors at a time and put the remaining factor under the ∛ .

∛128= 4∛2 

 We can find cube root of 128 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 128.

Step 1: Let a=128. Let us take x as 5, since, 5³=125 is the nearest perfect cube which is less than 128.

Step 2: Apply the formula.  ∛128≅ 5((5³+2×128) / (2(5)³+128))= 5.039…

Hence, 5.039… is the approximate cubic root of 128.
 

• Integers:  Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.

• 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 value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is the original number.

• 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.