Cube Root of 6

The cube root of 6 is 1.81712059283. The cube root of 6 is expressed as ∛6 in radical form, where the “ ∛ “  sign" is called the “radical” sign. In exponential form, it is written as (6)^1/3. If “m” is the cube root of 6, then, m³=6. Let us find the value of “m”.
 

The cube root of 6 is expressed as ∛6 as its simplest radical form. We can find cube root of 6 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 6.

Step 1: Let a=6. Let us take x as 1, since, 13=1 is the nearest perfect cube which is less than 6.

Step 2: Apply the formula.  ∛6≅ 1((1³+2×6) / (2(1)³+6))=1.625. Hence, 1.625 is the approximate cubic root of 6.
 

• 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.

 

• 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.