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Last updated on November 30th, 2024

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Cube Root of 100

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Foundation
Intermediate
Advance Topics

The cube root of 100 is the value that, when multiplied by itself three times (cubed), gives the original number 100. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, creating digital art, field of engineering, making financial decisions etc.

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What Is the 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”.

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Finding the Cube Root of 100

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.
 

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Cube Root of 100 By Halley’s Method

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.
 

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Important Glossaries for Cube 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.