# Properties of Radicals

• Simplify radical expressions using the product

rule for radicals

• Simplify radical expressions using the quotient

rule for radicals

**Simplified Form of a Radical**

A radical expression is in simplified form if all of the

following conditions are met:

1. The radicand has no factor raised to a

power greater than or equal to the index

2. There are no radicals in the denominator of

the fraction

3. The radicand does not contain a fraction.

**Simplifying Radical Expressions
Condition1**

**Simplify
**

**Simplify**

**Simplify**

**Product Rule for Radicals**

**Simplify**

**Simplify**

**Quotient Rule for Radicals
**

**Simplifying Radical Expressions**

Condition 2

Condition 2

**Simplify**

**Simplify**

**Simplify**

**Simplify**