1. Splash Screen

2. 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
Lesson Menu

3. A. 11h
B. 11h2
C. 13h2
D. –11h
5-Minute Check 1

4. A. 11h
B. 11h2
C. 13h2
D. –11h
5-Minute Check 1

5. A.
B. –4ay3 C.
D. 8ay3
5-Minute Check 2

6. A.
B. –4ay3 C.
D. 8ay3
5-Minute Check 2

7. A. B. C. D.
5-Minute Check 3

8. A. B. C. D.
5-Minute Check 3

9. A. |m – 4|
B. m – 4
C. |m – 2|
D. m – 2
5-Minute Check 4

10. A. |m – 4|
B. m – 4
C. |m – 2|
D. m – 2
5-Minute Check 4

11. A. about 1.43 m B. about 2.52 m C. about 3.11 m D. about 5.48 m
5-Minute Check 5

12. A. about 1.43 m B. about 2.52 m C. about 3.11 m D. about 5.48 m
5-Minute Check 5

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

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

15. Mathematical Practices
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.
CCSS

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

17. rationalizing the denominator like radical expressions conjugate
Vocabulary

18. Concept

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

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

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

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

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

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

25. A. B. C. D.
Example 1

26. A. B. C. D.
Example 1

27. Concept

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

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

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

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

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

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

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

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

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

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

38. Concept

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

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

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

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

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

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

45. A. B. C. D.
Example 4

46. A. B. C. D.
Example 4

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

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

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

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

51. 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 .
Example 6

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

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

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

55. 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.
Example 6

56. 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.
Example 6

57. End of the Lesson