1. Section 9.3 Multiplying and Dividing Radical Expressions

2. 9.3 Lecture Guide: Multiplying and Dividing Radical Expressions Objective: Multiply radical expressions.

3. To multiply and divide some radical expressions, we use the properties: Multiplying Radicals forand for and

4. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 1.

5. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 2.

6. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 3.

7. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 4.

8. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 5.

9. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 6.

10. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 7.

11. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 8.

12. Simplify each expression. Assume x > 0 and y > 0. 9.

13. Simplify each expression. Assume x > 0 and y > 0. 10.

14. Simplify each expression. Assume x > 0 and y > 0. 11.

15. Simplify each expression. Assume x > 0 and y > 0. 12.

16. Objective: Divide and simplify radical expressions.

17. Dividing Radicals When dividing radical expressions, we do not always get a result that is rational. In this case, answers are typically given without any radicals in the denominator. Recall that = ____________ for In general, _____________ for

18. As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 13.

19. As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 14.

20. As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 15.

21. As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 16.

22. Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 17.

23. Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 18.

24. Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 19.

25. Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 20.

26. Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 21.

27. Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 22.

28. Conjugates Radicals: The conjugate ofis

29. Write the conjugate of each expression. Then multiply the expression by its conjugate. ExpressionConjugateProduct 23. 24. 25. Example:

30. Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 26.

31. Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 27.

32. Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 28.

33. Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 29.

34. Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 30.

35. Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 31.

36. Determine whether or not each value of x is a solution of the equation 32.

37. Determine whether or not each value of x is a solution of the equation 33.

38. Determine whether or not each value of x is a solution of the equation 34.

39. Determine whether or not each value of x is a solution of the equation 35.