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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
of two factors, one of which is a perfect power
of the index.

Step 2: Write the radicand as the product of two
radicals, one of which contains perfect squares.

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 Radicals
If 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