This document discusses techniques for multiplying and dividing radical expressions. It covers multiplying radical expressions similar to polynomials using the FOIL method. It also covers rationalizing denominators by multiplying the numerator and denominator by a term to remove radicals from the denominator. Finally, it discusses writing radical quotients in lowest terms after factoring.

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Sec 9.5 - 1

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Sec 9.5 - 2
Roots, Radicals, and Root Functions
Chapter 9

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Sec 9.5 - 3
9.5
Multiplying and Dividing
Radical Expressions

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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.

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9.5 Multiplying and Dividing Radical Expressions
Multiply Radical Expressions
Multiplication of expressions that contain radicals is very
similar to multiplication of polynomials.

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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:

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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.