Cube Root of 25

The cube root of 25 is 2.92401773821. The cube root of 25 is expressed as ∛25 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (25)^1/3.  If “m” is the cube root of 25, then, m³=25.  Let us find the value of “m”.
 

The Prime Factorization of 25 is 5×5, so, the cube root of 25 is expressed as ∛25 as its simplest radical form. We can find the cube root of 25 through a method, named 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 25.

Step 1: Let a=25. Let us take x as 2, since, 2³=8 is the nearest perfect cube which is less than 25.

Step 2: Apply the formula.  ∛25≅ 2((2³+2×25) / (2(2)³+25))= 2.82…

Hence, 2.82… is the approximate cubic root of 25.
 

• 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. These cannot be in fractional or decimal form. 

• Square root -The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.

• 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, as if the approximate value is just near and close the original value.

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