Cube Root of 256

The cube root of 256 is 6.34960420787. The cube root of 256 is expressed as ∛256 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (256)^1/3. If “m” is the cube root of 256, then, m³=256. Let us find the value of “m”.
 

The cube root of 256 is expressed as 4∛4 as its simplest radical form, since

 256 = 2×2×2×2×2×2×2×2

∛256 = ∛(2×2×2×2×2×2×2×2)

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

∛256= 4∛4 

 We can find cube root of 256 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 256.

Step 1: Let a=256. Let us take x as 6, since, 6³=216 is the nearest perfect cube which is less than 256.

Step 2: Apply the formula.  ∛256≅ 6((6³+2×256) / (2(6)³+256))= 6.34

Hence, 6.34 is the approximate cubic root of 256.
 

• 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.

• Irrational numbers - The numbers which cannot be expressed in the form of “m/n”, where n ≠ 0 and m, n are integers.

• 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.