# Radical Expressions

### By: Marwan Mohamed

## What is a Radical Expression ??

The n'th root of a real number "A" can be written as the radical expression n√

*a ( N root A ). A radical expression includes a root sign.**"N" is called the index of the radical and "A" is called the radicand.**1) When a radical sign shows no index, it represents a square root.*

*2) When a number has more than one real root, the radical sign indicates only the principal or the positive root. *

## Undefined and Defined !!

Defined: Odd and even indices with positive radicands will produce real roots.

Undefined: While Even indices with negative radicands has no real roots.

## Operations with Radical Expressions

## Addition/ Subtraction Like Radicals can be added or subtracted normally. √
| ## Multiplications A product under a radical is equal to the product of the radicals.
√ | ## Divison A quotient under the radical is equal to the quotient of the radicals. √ |

## Simplification

## Note That !!

The rules of the exponent applies also for fractional exponents.

x^1/2 * x^1/2 = x^1

Algebra 2 - Operations on Radical Expressions