1. Including Rationalizing The Denominators

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

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

4. Multiplying Square Roots Multiply. Write the product in simplest form. Product Property of Square Roots. Multiply the factors in the radicand. Factor 16 using a perfect-square factor. Product Property of Square Roots Simplify. COPY

5. Multiplying Square Roots Multiply. Write the product in simplest form. Expand the expression. Commutative Property of Multiplication. Product Property of Square Roots. Simplify the radicand. Simplify the Square Root. Multiply. COPY

6. Multiplying Square Roots Multiply. Write the product in simplest form. Product Property of Square Roots. Factor 4 using a perfect-square factor. Take the square root.. Simplify. COPY

7. Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Multiply the factors in the radicand. Factor 25 using a perfect-square factor. Product Property of Square Roots Simplify.

8. Try This! Multiply. Write the product in simplest form. Expand the expression. Commutative Property of Multiplication. Product Property of Square Roots. Simplify the radicand. Simplify the Square Root. Multiply.

9. Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Factor 14 using a perfect-square factor. Take the square root. Simplify.

10. Using the Distributive Property Multiply. Write each product in simplest form. 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 COPY

11. Using the Distributive Property Multiply. Write the product in simplest form. Product Property of Square Roots. Distribute Simplify the radicands. Simplify.

12. Try This! Multiply. Write the product in simplest form. 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

13. Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Simplify the radicand. Simplify. Distribute COPY

14. Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Simplify the radicand. Simplify. Distribute

15. Try This! Multiply. Write each product in simplest form. Product Property of Square Roots. Simplify the radicand. Simplify. Distribute

16. 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.

17. Rationalizing the Denominator Simplify the quotient. Multiply by a form of 1 to get a perfect-square radicand in the denominator. Product Property of Square Roots. Simplify the denominator. COPY

18. Rationalizing the Denominator Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. COPY

19. Try This! Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator.

20. Try This! Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. COPY

21. Try This! 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. COPY

22. Lesson Quiz Multiply. Write each product in simplest form. 1. 3. Simplify each quotient. 5. 7. 8. 2. 4. 6.