1. Homework 1. 3. 5. 2. 4. 6. 7. Multiply. Write each product in simplest form. All variables represent nonnegative numbers. 8.9. Simplify each quotient. All variables represent nonnegative numbers.

2. Warm Up Simplify each expression. 1. 2. 3. 4.

3. You can use the Product and Quotient Properties of square roots you have already learned to multiply and divide expressions containing square roots.

4. Additional Example 1A: Multiplying Square Roots Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Product Property of Square Roots Multiply the factors in the radicand. Factor 16 using a perfect-square factor. Product Property of Square Roots Simplify.

5. Additional Example 1B: Multiplying Square Roots Expand the expression. Commutative Property of Multiplication Product Property of Square Roots. Simplify the radicand. Simplify the square root. Multiply. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

6. Additional Example 1C: Multiplying Square Roots Simplify the radicand. Factor 12 using a perfect-square factor. Product Property of Square Roots Simplify. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

7. Check It Out! Example 1a Product Property of Square Roots Multiply the factors in the radicand. Factor 50 using a perfect-square factor. Product Property of Square Roots Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

8. Check It Out! Example 1b Expand the expression. Commutative Property of Multiplication Product Property of Square Roots Simplify the radicand. Simplify the square root. Multiply. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

9. Check It Out! Example 1c Product Property of Square Roots Factor 14m. Product Property of Square Roots Simplify. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

10. Additional Example 2A: Using the Distributive Property Product Property of Square Roots. Multiply the factors in the second radicand. Factor 24 using a perfect-square factor. Product Property of Square Roots Simplify. Distribute Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

11. Additional Example 2B: Using the Distributive Property Product Property of Square Roots Distribute Simplify the radicands. Simplify. Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

12. Check It Out! Example 2a Product Property of Square Roots Multiply the factors in the first radicand. Factor 48 using a perfect-square factor. Product Property of Square Roots Simplify. Distribute Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

13. Check It Out! Example 2b Product Property of Square Roots Factor 50 using a perfect-square factor. Simplify. Distribute Multiply. Write the product in simplest form. All variables represent nonnegative numbers.

14. In Chapter 7, you multiplied binomials by using the FOIL method. The same method can be used to multiply square-root expressions that contain two terms.

15. First terms Outer terms Inner terms Last terms See Lesson 7-8. Remember!

16. = 20+ 3

17. Additional Example 3A: Multiplying Sums and Differences of Radicals Multiply. Write the product in simplest form. Use the FOIL method. Simplify the radicand. Simplify by combining like terms. Simplify.

18. Additional Example 3B: Multiplying Sums and Differences of Radicals Multiply. Write the product in simplest form. Expand the expression. Use the FOIL method. Simplify by combining like terms.

19. Check It Out! Example 3a Multiply. Write the product in simplest form. Expand the expression. Use the FOIL method. Simplify by combining like terms.

20. Check It Out! Example 3b Multiply. Write the product in simplest form. Use the FOIL method. Simplify by combining like terms.

21. A quotient with a square root in the denominator is not simplified. To simplify these expressions, multiply by a form of 1 to get a perfect-square radicand in the denominator. This is called rationalizing the denominator.

22. Additional Example 4A: Rationalizing the Denominator Simplify the quotient. All variables represent nonnegative numbers. Multiply by a form of 1 to get a perfect- square radicand in the denominator. Product Property of Square Roots Simplify the denominator.

23. Additional Example 4B: Rationalizing the Denominator Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. Simplify the quotient. All variables represent nonnegative numbers.

24. Use the square root in the denominator to find the appropriate form of 1 for multiplication. Helpful Hint

25. Check It Out! Example 4a Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator.

26. Check It Out! Example 4b Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator.

27. Check It Out! Example 4c Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. Factor and simplify the square root in the numerator.

28. Lesson Quiz 1. 3. 5. 2. 4. 6. 7. Multiply. Write each product in simplest form. All variables represent nonnegative numbers. 8.9. Simplify each quotient. All variables represent nonnegative numbers.