1. Splash Screen Unit 6 Exponents and Radicals

2. Splash Screen Essential Question: How do you simplify radical expressions?

3. In this lesson, work will be done with radicals, specifically square root radicals, such as _____ or _____.

4. What is a RADICAL? If n is a positive integer that is greater than 1 and a is a real number then, where n is called the index, a is called the radicand, and the symbol √ is called the radical.

5. 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 11 2 = 121 12 2 = 144 13 2 = 169 14 2 = 196 15 2 = 225 Perfect Squares Know these!

6. Square Root - easy definition A number that when multiplied by itself equals a given number. Root A number that, when multiplied by itself some number of times, equals a given number.

7. Then/Now You simplified radicals. Simplify radical expressions by using the Product Property of Square Roots. Simplify radical expressions by using the Quotient Property of Square Roots. EQ: How do simplify radical expressions?

8. Vocabulary radical expression rationalizing the denominator

9. A radicand is in simplest form if the following 3 conditions are true. No radicands have _________ square factors other than 1. perfect #1

10. A radicand is in simplest form if the following 3 conditions are true. No radicands contain ______________. fractions #2

11. A radicand is in simplest form if the following 3 conditions are true. No radicals appear in the denominator of a ______________. fraction #3

12. Concept 1

13. A radicand is in simplest form if the following 3 conditions are true. No radicands have _________ square factors other than 1. perfect #1

14. Example 1 Simplify Square Roots

15. Example 1 Simplify Square Roots

16. Example 1 Simplify Square Roots

17. Example 1 Simplify Square Roots

18. Example 1 Simplify Square Roots

19. Example 1 Simplify Square Roots

20. Example 1 Simplify Square Roots

21. Example 1 Simplify Square Roots

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

23. Concept 1 A. B. C. D. Do these examples on the practice worksheet.

24. Example 2 Multiply Square Roots

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

28. Concept 1 E. F. G. H. Do these examples on the practice worksheet.

30. Example 3 Simplify a Square Root with Variables Prime factorization Product Property Simplify. Answer:

31. Example 3 A. B. C. D.

32. I. Do these examples on the practice worksheet.

33. J. Do these examples on the practice worksheet.

34. K. Do these examples on the practice worksheet.

35. L. Do these examples on the practice worksheet.

36. End of the Lesson Assignment: Do #1 to #34 on the Practice Worksheet

37. Concept 2

38. A radicand is in simplest form if the following 3 conditions are true. No radicands contain ______________. fractions #2

39. A radicand is in simplest form if the following 3 conditions are true. No radicals appear in the denominator of a ______________. fraction #3

40. Concept 2 Multiplying by 1 does not change it’s value. Rationalizing the Denominator

41. Multiplying by 1 does not change it’s value. Rationalizing the Denominator

42. Multiplying by 1 does not change it’s value. Rationalizing the Denominator

44. Example 4 A. B. C. D.

51. Example 4 Which expression is equivalent to ? AC BDAC BD

52. M. N. Do these examples on the practice worksheet.

53. O. P. Do these examples on the practice worksheet.

55. End of the Lesson Assignment: Complete the Practice Worksheet