# Simplify Radical Expressions

**7.3: Simplify Radical Expressions**

**Learning Objectives:
**1. Use the product property to multiply

radical expressions.

2. Use the product property to simplify

radical expressions.

3. Use the quotient property to simplify

radical expressions.

4. Multiply radicals with unlike indices.

**1. The Product Property**

**2. Simplifying Radical Expressions**

A radical expression is **simplified** provided that the

radicand does not contain any factors that are perfect

powers of the index.

Simplifying a Radical Expression
Step 1: Write each factor of the radicand as the
product Step 2: Write the radicand as the product of two Step 3: Take the nth root of each perfect power. |

**Example**: Simplify the following:

**Example:**

Simplify the following:

**3. The Quotient Property**

Quotient Property of RadicalsIf and are real numbers, b ≠ 0, and n ≥ 2 is an integer, then |

**Example: **Simplify:

**Simplifying Radical Expressions**

**Example:** Simplify:

**Example: **Simplify:

**Example:** Multiply and simplify.

**4. Multiplying with Unlike Indices**