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Last updated on ** October 1st, 2024**

The cube root of 128 is the value that, when multiplied by itself three times (cubed), gives the original number 128. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.

The cube root of 128 is 5.03968419958. The cube root of 128 is expressed as β128 in radical form, where the “β" sign is called the “radical” sign. In exponential form, it is written as (128)^{β
}. If “m” is the cube root of 128, then, m^{3}=128. Let us find the value of “m”.

The cube root of 128 is expressed as 4β2 as its simplest radical form,

since 128 = 2×2×2×2×2×2×2

β128 = β(2×2×2×2×2×2×2)

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

β128= 4β2

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, x^{3}=N, where this method approximates the value of “x”.

Formula is βa≅ x((x^{3}+2a) / (2x^{3}+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. β128≅ 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 β€« 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.