Cube Root of 18

The cube root of 18 is the value which, when multiplied by itself three times (cubed), gives the original number 18. The cube root of 18 is 2.62074139421.  The cube root of 18 is expressed as ∛18 in radical form, where the “ ∛ ”  sign” is called the “radical” sign. In exponential form, it is written as (18)^⅓. If “m” is the cube root of 18, then, m³=18. Let us find the value of “m”.
 

We can find cube root of 18 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 18.

Step 1: Let a=18. Let us take x as 2, since 2³=8 is the nearest perfect cube which is less than 18.

Step 2: Apply the formula.  ∛18≅ 2((2³+2×18) / (2(2)³+18))= 2.59…

Hence, 2.59… is the approximate cubic root of 18.
 

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

• Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be found out.

• 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 near to the correct answer, but not perfectly correct.

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