1. Multiplying, Dividing, and Simplifying Radicals 10.3 1.Multiply radical expressions. 2.Divide radical expressions. 3.Use the product rule to simplify radical expressions.

2. Product Rule for Radicals If both and are real numbers, then The index (root) must be the same!

3. Multiply:

4. Quotient Rule for Radicals If both and are real numbers, then

5. Divide:

6. Divide:

7. 1 4 9 16 25 36 49 64 81 100 Simplify radicals: Look for the largest perfect square that divides into the radicand evenly.

8. Simplify radicals: 1 4 9 16 25 36 49 64 81 100 Create a factor tower.

9. Divide by prime numbers! 2, 3, 5, 7, 11, …

12. Simplify radicals: 1 4 9 16 25 36 49 64 81 100

13. 1 4 9 16 25 36 49 64 81 100 Simplify radicals:

14. 1 4 9 16 25 36 49 64 81 100 Simplify radicals:

15. 1 4 9 16 25 36 49 64 81 100 Simplify radicals:

16. Slide 10- 16 Copyright © 2011 Pearson Education, Inc. Simplify. a) b) c) d)

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

18. Simplify radicals: Outside Inside Outside Inside Think…

19. Simplify radicals: Outside Inside Think:

20. Simplify: 25∙3

21. Simplify: 16∙3

22. 1 8 27 64 125 216 343 Simplify radicals:

23. 1 8 27 64 125 216 343 Simplify radicals:

24. Simplify: 8∙3

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

26. Simplify: 16∙3 1 4 9 16 25 36 49 64 81 100

27. Slide 10- 27 Copyright © 2011 Pearson Education, Inc. Simplify. a) b) c) d)

28. Slide 10- 28 Copyright © 2011 Pearson Education, Inc. Simplify. a) b) c) d)