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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Simplify Radical Expressions

7.3: Simplify Radical Expressions

Learning Objectives:
1. Use the product property to multiply

2. Use the product property to simplify

3. Use the quotient property to simplify

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: Example: Simplify: Example: Simplify: Example: Multiply and simplify. 4. Multiplying with Unlike Indices 