1. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 15 Roots and Radicals

2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 15.4 Multiplying and Dividing Radicals

3. Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. If and are real numbers, then Product Rule for Radicals

4. Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. Then simplify the product if possible. Example

5. Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. b. Example

6. Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. If and are real numbers and b ≠ 0, then Quotient Rule for Radicals

7. Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Divide. The simplify the quotient if possible. Example

8. Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Many times it is helpful to rewrite a radical quotient with the radical confined to ONLY the numerator. If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator. This process involves multiplying the quotient by a form of 1 that will eliminate the radical in the denominator. Rationalizing Denominators

9. Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rationalize the denominator. a. b. Example

10. Martin-Gay, Developmental Mathematics, 2e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical. In that case, we need to multiply by the conjugate of the numerator or denominator (which ever one we are rationalizing). The conjugate uses the same terms, but the opposite operation (+ or –). Conjugates

11. Martin-Gay, Developmental Mathematics, 2e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rationalize the denominator. Example