1. + Warm Up #2

2. + HW Check – Exponents Practice

3. + 7.1 Simplifying Radical Expressions

4. + Nth Root For any real number a and b, and any positive integer n, if a n = b, then a is the n th root of b.

5. +

6. + Real Number Examples: Find the roots: 1. Square Root of 4 Square Root of -4 2. Cube Root of 8Cube Root of -8 Even Index, Negative Radican = No Real Solution Odd Index, Negative Radican = Negative Solution

7. + Simplifying Radical Numbers - Find the largest perfect square/cube factor. - Take the square/cube of the factor, goes on the outside - Leftover factor stays INSIDE the radical.

8. + Variable Examples: For variables you take GROUPS of the index out, leaving the remainder in!

9. + Simplify : 1. 2.

10. + 3. 4.

11. + 5. 6.

12. + 7. 8. 9.

13. + 10. 11. 12.

14. + Warm Up

15. + Section 7.2 Multiplying & Dividing Radicals

16. + Multiplying Radical Expressions If they are real numbers, then

17. + Examples: 1. 2.

18. + 3. 4.

19. + 5. 6.

20. + Dividing Radical Expressions

21. + Examples: 1.2.

22. + Rationalizing the Denominator **Multiply the numerator and denominator by the denominator** Then Simplify Example: 1. No square roots in the denominator!

23. + 2. 3.

24. + Warm Up #3

25. + HW Check – 7.2 Odds

26. + 7.3 Adding, Subtracting, Multiplying and Dividing Binomial Radical Expressions

27. + Adding Radical Expressions Use the same concept as that of adding or subtracting like variables. Example: 7 - 3x + 2x + 5 *Have to have like Terms to Add/Subtract*

28. + Like Radicals are radical expressions that have the same index and the same radicand.

29. + Like RadicalsUnlike Radicals=

30. + Examples: 1. 2.

31. + 3. 4. 5. 6.

32. + Always simplify radicals before combining! 1.2.

33. + 3. 4. 5.

34. + Multiplying Binomials To multiply, USE FOIL! Example 1:

35. + 2.3.

36. + Dividing Binomial Radicals To divide, Rationalize the denominator! (a + b)( a - b) = a 2 – b 2 These are called conjugates! They make radicals disappear!

37. + Examples: 1.

38. + 2.

39. + Examples: 1.

40. + 2.

41. + 3.

42. + 4.

43. + 7.4 Rational Exponents

44. + Rational Exponents

45. + Rational Exponents are another way to write radicals.

46. + Simplify each expression. 1. 2.

47. + 3.

48. + 4.5.

49. + 6.

50. + Rational Exponents to Radicals The Denominator is the INDEX The Numerator is the POWER

51. + Converting to Radical Form 1. 2.

52. + 3. 4. 5.

53. + Converting to Exponential Form 1. 2.

54. + 3. 4. 5.

55. + Properties of Exponents also apply to Rational Exponents! Write in Radical Form:

56. + 2. 3. 4. 5.

57. + Simplify each expression. 1. 2.

58. + 3. 4.

59. + Warm Up #4

60. + HW Check – 7.4

61. + 7.5 Solving Radical Equations

62. + Radical Equations A radical equation is an equation that has a variable in a radicand or has a variable with a rational exponent. Are these Radical Equations?

63. + We use inverse operations to solve equations. Solve: X 2 = 4

64. + What is the inverse of cubing x? Solve: X 3 = 64

65. + Solve the following. Check your solutions! 1.2.

66. + 6.

67. + Solve (x) 1/2 = 3 **To solve radical equations with rational exponents, raise each side to the reciprocal exponent!

68. + Examples: 1.2.

69. + Solve 3.4.

70. + 1.

71. + 3. 4.

72. + You can also solve by graphing! Given: The equation is already equal to zero! y= Find the x-intercept!