Multiplying & Simplifying Radical Expressions

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Presentation transcript:

Multiplying & Simplifying Radical Expressions KM & PP 1 1

Finding Square Roots Definition 8.2 S KM & PP

Remember! The Square Root of Apple Squared is Apple! 8.2 S KM & PP

Notice! AND 8.2 S KM & PP 4

Notice! 8.2 S KM & PP 5

The Product Rule for Radicals. The product of square roots is the square root of the product of the radicands AB of nonnegative radicands A & B. 8.2 S KM & PP

The Product Rule for Radicals. EXAMPLES: Multiply 8.2 S KM & PP 7

Radical Expressions. How about? 8.2 S KM & PP

Radical Expressions. Check the definition 8.2 S KM & PP

Check: x3x3=x3+3=x6 Check: x6x6=x6+6=x12 Try Two! Examples 4 & 5 8.2 S KM & PP

Notice a Pattern? 8.2 S KM & PP

Notice a Pattern? 8.2 S KM & PP

You try. Example 6 Check: x17x17=x17+17=x34 8.2 S KM & PP

You try. Example 7 Check: x31x31=x31+31=x62 8.2 S KM & PP 14

Notice! 8.2 S KM & PP

Factoring Radical Expressions. KM & PP

Factoring Radical Expressions. EXAMPLES: Simplify 8.2 S KM & PP 17

How About? 8.2 S KM & PP

Introduction to Radical Expressions. Even exponents are squares. Odd exponents can be factored to even exponents times x. 8.2 S KM & PP

In Other Words The Square Root of Apple Cubed is Apple times KM & PP

You Try. Example 9 8.2 S KM & PP

You Try. Example 10 8.2 S KM & PP

More Problems. Example 11 8.2 S KM & PP

More Problems. Example 12 8.2 S KM & PP

One More. Example 13 8.1 S KM & PP

Another Square Root! Example 16 KM & PP

More Problems. Example 17 8.2 S KM & PP

Factoring Again. Example 17 8.2 S KM & PP

The Product Rule for Radicals Basics Simplify After Multiplying. Leave the Radicand in Factored Form. Factor Further to find Perfect-square factors. Simplify using the perfect-square factors. 8.2 S KM & PP

The Product Rule for Radicals. EXAMPLE 18: Multiply 8.2 S KM & PP 30

The Product Rule for Radicals. Another Approach EXAMPLE 18: Multiply 8.2 S KM & PP 31

Remember! One gets shot during the escape. The Radical is like a prison. It takes two to escape. 8.2 S KM & PP 32 32

The Product Rule for Radicals. EXAMPLE 19: Multiply 8.2 S KM & PP 33

The Product Rule for Radicals. Another Approach EXAMPLE 19: Multiply 8.2 S KM & PP 34

That’s All for Now! 8.1 S KM & PP