1. Over Lesson 6–4 5-Minute Check 1 A.11h B.11h 2 C.13h 2 D.–11h

2. Over Lesson 6–4 5-Minute Check 2 A. B.–4ay 3 C. D.8ay 3

3. Concept

4. Example 1 Simplify Expressions with the Product Property Factor into squares where possible. Product Property of Radicals Answer:Simplify.

5. Example 1 Simplify Expressions with the Product Property Factor into cubes. Product Property of Radicals Simplify. Answer:

6. Example 1 A. Simplify. A. B. C. D.

7. Example 1 A. B. C. D.

8. Concept

9. Example 2 Simplify Expressions with the Quotient Property Quotient Property Factor into squares. Product Property A.

10. Example 2 Simplify Expressions with the Quotient Property Answer: Rationalize the denominator.

11. Example 2 Simplify Expressions with the Quotient Property Quotient Property Product Property Rationalize the denominator.

12. Example 2 Simplify Expressions with the Quotient Property Answer: Multiply.

13. Example 2 A. Simplify. A. B. C. D.

14. Example 2 B. Simplify A. B. C. D.

15. Concept

16. Example 3 Multiply Radicals = 5 ● 10 ● a or 50aMultiply. Product Property of Radicals Factor into cubes where possible. Product Property of Radicals Answer:5 ● 10 ● a or 50a

17. Example 3 A.12a B.24a C.4a D.6a

18. Example 4 Add and Subtract Radicals Factor using squares. Product Property Multiply. Combine like radicals. Answer:

19. Example 4 A. B. C. D.

20. Example 5 Multiply Radicals Simplify. F O I L Product Property Answer:

21. Example 5 A. B. C. D. Simplify.

22. Example 6 Use a Conjugate to Rationalize a Denominator GEOMETRY In a square with side a, the ratio of a side to the difference between the diagonal and a side is. Use a conjugate to rationalize the denominator and simplify.

23. Example 6 Use a Conjugate to Rationalize a Denominator Multiply. Simplify. Factor out the GCF.

24. Example 6 Use a Conjugate to Rationalize a Denominator Simplify.

25. Example 6 GEOMETRY In the triangle shown with height x, the ratio of the height to the base is. Use a conjugate to rationalize the denominator and simplify. A.B. C.D.