1.  An n th root ( ) of b is a solution of the equation. Roots of Real Numbers n is even n is odd If b>0, two real roots. Principal root is positive. If b<0, no real roots. If b>0, or b<0, there is exactly one real root.

2.  Simplify the following roots: Roots of Real Numbers

3.  What is the difference between the following expressions? Roots of Real Numbers

4.  What is the difference between the following expressions? Roots of Real Numbers

5.  Simplify the following: Roots of Real Numbers

6. Learning Log Summary LT 1 – I can identify the roots of real numbers. The n th root is… If a negative number is in an odd/even root…

7. Closure Homework (record on Learning Log): LT 1: pg. 262 ~ 1-13 (Odd) pg. 263 ~ Mixed Review 1-5

8.  Consider: and  Complete the following property of radicals: Simplifying Radicals

9.  Consider: and  Complete the following property of radicals: Simplifying Radicals

10.  The properties we just discovered DO NOT apply to addition and subtraction. CAUTION!!!!

11.  Simplify: Simplifying Radicals

12.  Rationalizing the Denominator means to re-write a fraction with a radical in the denominator so that the only radical is in the numerator.  To accomplish this, multiply by some form of 1 so that the denominator can be simplified without a radical. Ex 1) Ex 2) Simplifying Radicals

13. Learning Log Summary LT 2 – I can simplify expressions involving radicals. To simplify a number without the given root… Rationalizing the denominator means…

14. Closure Homework (record on Learning Log): LT 2: pg. 267 ~ 1-31 (O), 39-45 (O)

15. CONNECT 4 Place any of the items from the answer bank into any space of your Connect 4 board without repeating. You will not use all of the answers! Solve each problem, and if the answer is on the board, place an X in the space. First three people to Connect 4 win!

16. Connect 4 Simplify:

17. Connect 4 Simplify:

18. Connect 4 Simplify:

19. Connect 4 Simplify:

20. Connect 4 Simplify:

21. Connect 4 Simplify:

22. Connect 4 Simplify:

23. Connect 4 Simplify:

24. Connect 4 Simplify:

25. Connect 4 Simplify:

26. Connect 4 Simplify:

27. Connect 4 Simplify:

28. Connect 4 Simplify:

29. Connect 4 Simplify:

30. Connect 4 Simplify:

31. Checkpoint #1

32. Checkpoint #2

33. Checkpoint #3

34. Checkpoint #4

35. Learning Log Summary LT 3 – I can simplify expressions involving the sum of radicals. In order to add or subtract radicals… Roots that can be added or subtracted…

36. Closure Homework (record on Learning Log): LT 3: pg. 272 ~ 1-25 (O)

37. Multiplying / Dividing Radical Expressions Simplify the following:

38. Multiplying / Dividing Radical Expressions Simplify the following:

39. Multiplying / Dividing Radical Expressions Simplify the following:

40. Conjugates Notice that the value of is an integer. Expressions of the form and are called conjugates. Multiplying by a conjugate “eliminates” the radicals.

41. Multiplying / Dividing Radical Expressions Simplify the following:

42. Multiplying / Dividing Radical Expressions Simplify the following:

43. Learning Log Summary LT 4 – I can simplify the product and quotients of binomials that contain radicals. When multiplying radicals… If the denominator of a fraction contains a radical expression…

44. Closure Homework (record on Learning Log): LT 4: pg. 275 ~ 1-29 (O)

45. Solving Radical Equations Any equation that contains a variable in the radicand is called a radical equation. For example: As a non-example:

46. Solving Radical Equations REVIEW – What is an extraneous solution ? For Example:

47. Solving Radical Equations Solve:

48. Solving Radical Equations Solve:

49. Learning Log Summary LT 5 – I can solve equations involving radicals. To solve a radical equation… LT 6 – I can identify extraneous solutions to radical equations, using appropriate justifications. An extraneous solution is…

50. Closure Homework (record on Learning Log): LT 5/6: pg. 280 ~ 1-19 (O) pg. 282 ~ 1-12 (all) QUIZ on MONDAY on LT 1-6