Copyright 2010 Pearson Education Inc All rights reserved

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9. 5 - 1

Chapter 9 Roots, Radicals, and Root Functions Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9. 5 - 2

9. 5 Multiplying and Dividing Radical Expressions Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9. 5 - 3

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. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9. 5 - 4

9. 5 Multiplying and Dividing Radical Expressions Multiply Radical Expressions Multiplication of expressions that contain radicals is very similar to multiplication of polynomials. 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. 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. FOIL Method Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9. 5 - 7

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. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9. 5 - 8

9. 5 Multiplying and Dividing Radical Expressions Rationalize Denominators with Square Roots Rationalize the following: Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9. 5 - 9

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. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9. 5 - 10

9. 5 Multiplying and Dividing Radical Expressions Rationalize Denominators with Binomials Involving Radicals 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 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 Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9. 5 - 13

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. 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. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9. 5 - 15