Cube Root of 10

The cube root of 10 is 2.15443469003. The cube root of 10 is expressed as ∛10 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (10)^1/3. If “m” is the cube root of 10, then, m³=10. Let us find the value of “m”.
 

The cube root of 10 is expressed as ∛10 as its simplest radical form. We can find cube root of 10 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 10.

Step 1: Let a=10. Let us take x as 2, since, 2³=8 is the nearest perfect cube which is less than 10.

Step 2: Apply the formula.  ∛10≅ 2((2³+2×10) / (2(2)³+10))=2.15

Hence, 2.15 is the approximate cubic root of 10.
 

• Irrational Numbers - Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.

• 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.