2. Roots, Radicals, and Root Functions
Chapter 9
Roots, Radicals, and Root Functions

3. Multiplying and Dividing Radical Expressions
9.5
Multiplying and Dividing
Radical Expressions

4. 9.5 Multiplying and Dividing Radical Expressions
Objectives
Multiply radical expressions.
Rationalize denominators with one radical term.
Rationalize denominators with binomials involving radicals.
Write radical quotients in lowest terms.
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5. 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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6. 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.

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
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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.
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9. 9.5 Multiplying and Dividing Radical Expressions
Rationalize Denominators with Square Roots
Rationalize the following:
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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.
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11. 9.5 Multiplying and Dividing Radical Expressions
Rationalize Denominators with Binomials Involving Radicals
Copyright © 2010 Pearson Education, Inc. All rights reserved.

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

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

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.
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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.
Copyright © 2010 Pearson Education, Inc. All rights reserved.