1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 6–4) CCSS Then/Now New Vocabulary Key Concept: Product Property of Radicals Example 1: Simplify Expressions with the Product Property Key Concept: Quotient Property of Radicals Example 2: Simplify Expressions with the Quotient Property Concept Summary: Simplifying Radical Expressions Example 3: Multiply Radicals Example 4: Add and Subtract Radicals Example 5: Multiply Radicals Example 6: Real-World Example: Use a Conjugate to Rationalize a Denominator

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

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

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

6. Over Lesson 6–4 5-Minute Check 4 A.|m – 4| B.m – 4 C.|m – 2| D.m – 2

7. Over Lesson 6–4 5-Minute Check 5 A.about 1.43 m B.about 2.52 m C.about 3.11 m D.about 5.48 m

8. Over Lesson 6–4 5-Minute Check 6 A.10 and 11 B.11 and 12 C.12 and 13 D.13 and 14 Between which two whole numbers is ?

9. CCSS Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Mathematical Practices 1 Make sense of problems and persevere in solving them.

10. Then/Now You simplified expressions with nth roots. Simplify radical expressions. Add, subtract, multiply, and divide radical expressions.

11. Vocabulary rationalizing the denominator like radical expressions conjugate

12. Concept

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

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

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

16. Example 1 A. B. C. D.

17. Concept

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

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

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

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

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

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

24. Concept

25. 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

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

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

28. Example 4 A. B. C. D.

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

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

31. 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.

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

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

34. 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.

35. End of the Lesson