Cube Root of 2

The cube root of 2 is 1.25992104989. The cube root of 2 is expressed as ∛2 in radical form, where the “∛"  sign is called the “radical” sign. In exponential form, it is written as (2)^⅓. If “m” is the cube root of 2, then, m³=2. Let us find the value of “m”.
 

The Prime Factorization of 2 is 2×1, so, the cube root of 2 is expressed as ∛2 as its simplest radical form. We can find cube root of 2 through another 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 9.

Step 1: Let a=2. Let us take x as 1, since, 1³=1 is the nearest perfect cube which is less than 2.

Step 2: Apply the formula.  ∛2≅ 1((1³+2×2) / (2(1)³+2))=1.25

Hence, 1.25 is the approximate cubic root of 2.
 

• 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. Ex: 1,2,3,.... 

• 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 arithmetic operations like 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. It is just near to the exact value.

• 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.