1. Chapter 8 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. More Simplifying and Operations with Radicals Simplify products of radical expressions. Use conjugates to rationalize denominators of radical expressions. Write radical expressions with quotients in lowest terms. 1 1 3 3 2 28.58.5

3. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More Simplifying and Operations with Radicals Slide 8.5 - 3 The conditions for which a radical is in simplest form were listed in the previous section. A set of guidelines to use when you are simplifying radical expressions follows:

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More Simplifying and Operations with Radicals (cont’d) Slide 8.5 - 4

5. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Simplify products of radical expressions. Slide 8.5 - 5

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1A Find each product and simplify. Solution: Multiplying Radical Expressions (cont’d) Slide 8.5 - 6

7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1B Find each product and simplify. Solution: Multiplying Radical Expressions Slide 8.5 - 7

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find each product. Assume that x ≥ 0. EXAMPLE 2 Solution: Using Special Products with Radicals Slide 8.5 - 8 Remember only like radicals can be combined!

9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Using a Special Product with Radicals. Example 3 uses the rule for the product of the sum and difference of two terms, Slide 8.5 - 9

10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Using a Special Product with Radicals Slide 8.5 - 10 Find each product. Assume that Solution:

11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Use conjugates to rationalize denominators of radical expressions. Slide 8.5 - 11

12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The results in the previous example do not contain radicals. The pairs being multiplied are called conjugates of each other. Conjugates can be used to rationalize the denominators in more complicated quotients, such as Use conjugates to rationalize denominators of radical expressions. Slide 8.5 - 12 To simplify a radical expression, with two terms in the denominator, where at least one of the terms is a square root radical, multiply numerator and denominator by the conjugate of the denominator.

13. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4A Using Conjugates to Rationalize Denominators Slide 8.5 - 13 Simplify by rationalizing each denominator. Assume that Solution:

14. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4B Using Conjugates to Rationalize Denominators (cont’d) Slide 8.5 - 14 Simplify by rationalizing each denominator. Assume that Solution:

15. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Slide 8.5 - 15 Write radical expressions with quotients in lowest terms.

16. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Write in lowest terms. Solution: Writing a Radical Quotient in Lowest Terms Slide 8.5 - 16