Radical Formula with Solved Examples

Introduction

A Radical is a number that is similar to the root of a number. The root can be a square root, cube root, or in general, nth root. Therefore, any number or expression that uses a root is known as a radical. The term radical has been derived from the Latin word radix which means root. The radical could be defined in different kinds of roots for a number such as square root, cube root, nth root, fourth root, etc. The number is written before the radical is called an index number. The index number helps us in telling how many times the number would be multiplied by itself to get an equivalent radical. This is regarded as the opposite of exponent just like subtraction is the opposite of addition.

For instance, √125 = 5 as 5×5×5 = 125

General Rules of Radicals

The rules of Radicals are as follows:

• If the number is negative under the radical then its result will the negative. If the number is positive under the radical then the result will come in positive

• If the number under Radical is negative and the index is in an even number then the result will be an irrational number

• If the index number is not mentioned then the radical will be a square root

• Multiplication of numbers under similar index numbers and radicals is possible

• Under similar radical division is possible

• The opposite multiplication rule is also possible where similar radical splits

• The radical can be written in its exponent form in any Equation

• The inverse exponent of the index number is equal to the radical itself

Radical Formula

To solve a Radical Equation, one must make the Equation Radical free.

To make Equation nth root Radical free on both sides Equation with ‘n’.

n√x = p

x1/n = p

(x 1/n)n = p

x = pn

Where,

• n√ is used to represent the nth root

• n is known as the index number

• The variable inside the radical is known as radicand

Solved Example

Example 1 

Solve the radical expression (6 + 3√x)/y. Where x = 16 and y = 2

Given, that x = 16, y = 2

= (6 + 3√x)/y

= (6+3√16)/2

= 9

Therefore, the Radical expression is 9.

Example 2 

Solve the radical expression (8+4√x)/y. Where x = 25 and y = 4

Given x = 25 and y = 4

= (8+4√x)/y

= (8+4√25)/4

= (8+20)/4

= 7

Thus, the Radical expression is 7

Important Formulas: