Cube Root of 100

The cube root of 100 is 4.64158883361. The cube root of 100 is expressed as ∛100 in radical form, where the “ ∛ ”  sign  is called the “radical” sign. In exponential form, it is written as (100)^⅓. If “m” is the cube root of 100, then, m³=100. Let us find the value of “m”.

The cube root of 100 is expressed as ∛100 as its simplest radical form,

since 100 = 2×2×5×5

∛100 = ∛(2×2×5×5)

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

∛100= ∛100 

 We can find cube root of 100 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 100.

Step 1: Let a=100. Let us take x as 4, since, 4³=64 is the nearest perfect cube which is less than 100.

Step 2: Apply the formula.  ∛100≅ 4((4³+2×100) / (2(4)³+100))= 4.63…

Hence, 4.63… is the approximate cubic root of 100.
 

• Integers: Integers can be a positive natural number, a 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 that is nearly correct, but not perfectly correct.

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