1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.5 - 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.5 - 2 Roots, Radicals, and Root Functions Chapter 9

3. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.5 - 3 9.5 Multiplying and Dividing Radical Expressions

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 4 9.5 Multiplying and Dividing Radical Expressions Objectives 1.Multiply radical expressions. 2.Rationalize denominators with one radical term. 3.Rationalize denominators with binomials involving radicals. 4.Write radical quotients in lowest terms.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 5 9.5 Multiplying and Dividing Radical Expressions Multiply Radical Expressions Multiplication of expressions that contain radicals is very similar to multiplication of polynomials.

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 6 9.5 Multiplying and Dividing Radical Expressions Multiply Radical Expressions Multiplication of expressions that contain radicals is very similar to multiplication of polynomials.

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 7 9.5 Multiplying and Dividing Radical Expressions Multiply Radical Expressions Multiplication of expressions that contain radicals is very similar to multiplication of polynomials. FOIL Method

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 8 9.5 Multiplying and Dividing Radical Expressions Rationalize Denominators with One Radical Term A simplified radical expression has no radical in the denominator. The process of removing a radical from the denominator of a fractional expression is called rationalizing the denominator.

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 9 9.5 Multiplying and Dividing Radical Expressions Rationalize Denominators with Square Roots Rationalize the following:

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 10 9.5 Multiplying and Dividing Radical Expressions Rationalize Denominators with Cube Roots To rationalize a denominator with a cube root, we must multiply the numerator and denominator by a number that will result in a perfect cube.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 11 9.5 Multiplying and Dividing Radical Expressions Rationalize Denominators with Binomials Involving Radicals

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 12 9.5 Multiplying and Dividing Radical Expressions Rationalize Denominators with Binomials Involving Radicals

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 13 9.5 Multiplying and Dividing Radical Expressions Rationalize Denominators with Binomials Involving Radicals

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 14 9.5 Multiplying and Dividing Radical Expressions Writing Radical Quotients in Lowest Terms CAUTION Be careful to factor before writing a quotient in lowest terms.

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.5 - 15 9.5 Multiplying and Dividing Radical Expressions Writing Radical Quotients in Lowest Terms CAUTION Be careful to factor before writing a quotient in lowest terms.