1. Section 10.3 Multiplying and Dividing Radical Expressions

2. 10.3 Lecture Guide: Multiplying and Dividing Radical Expressions Objective 1: Multiply radical expressions.

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

4. Perform each indicated multiplication, and then simplify the product. Use your calculator to evaluate the original expression and your answer as a check on your answer. 1.

5. Perform each indicated multiplication, and then simplify the product. Use your calculator to evaluate the original expression and your answer as a check on your answer. 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. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 9.

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

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

15. Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 12.

16. Conjugates Radicals: The conjugate of is

17. Write the conjugate of each expression. Then multiply the expression by its conjugate. HINT: Review the special product ( ) ExpressionConjugateProduct 13. 14. 15.

18. Objective 2: Divide and simplify radical expressions.

19. 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

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

21. As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 17.

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

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

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

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

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

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

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

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

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.