Simplify Radical Expressions
7.3: Simplify Radical Expressions
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
Step 2: Write the radicand as the product of two
Step 3: Take the nth root of each perfect power.
Example: Simplify the following:
Simplify the following:
3. The Quotient Property
|Quotient Property of Radicals
If and are real numbers, b ≠ 0, and n ≥ 2 is an integer,
Simplifying Radical Expressions
Example: Multiply and simplify.
4. Multiplying with Unlike Indices