1. Rationalizing Numerators and Denominators of Radical Expressions 10.5 1.Rationalize denominators. 2.Rationalize denominators that have a sum or difference with a square root term. 3.Rationalize numerators.

3. Rationalize the denominator Irrational number Rational number

4. Rationalize: Factors or terms?

5. Rationalize: 1 4 9 16 25 36 49 64 81 100 2 1 3 1

6. Rationalize: 1 4 9 16 25 36 49 64 81 100

7. Rationalize: 1 4 9 16 25 36 49 64 81 100

8. 1 8 27 64 125 216 343 Rationalize:

9. Slide 10- 9 Copyright © 2011 Pearson Education, Inc. Rationalize the denominator. a) b) c) d)

10. Slide 10- 10 Copyright © 2011 Pearson Education, Inc. Rationalize the denominator. a) b) c) d)

11. Rationalize: Can I still multiply by ? No! Can I square the denominator? No! Try conjugates. To rationalize BINOMIAL denominators, use the conjugate! Binomial Denominator

12. Rationalize: Conjugates

13. Rationalize: Factors or terms? 4∙6 4∙10 5 3 Binomial Denominator All three!!!

14. Rationalize: Binomial Denominator

15. Rationalize the numerator:

17. Slide 10- 17 Copyright © 2011 Pearson Education, Inc. Rationalize the denominator. a) b) c) d)

18. Slide 10- 18 Copyright © 2011 Pearson Education, Inc. Rationalize the denominator. a) b) c) d)