1. Section 7.1
Rational Exponents and Radicals

2. OBJECTIVES A
Find the nth root of a number, if it exists.

3. OBJECTIVES B
Evaluate expressions containing rational exponents.

4. OBJECTIVES C
Simplify expressions involving rational exponents.

5. DEFINITION
NTH ROOT
If a and x are real numbers and n is a positive integer:
x is an nth root of a if xn = a

6. DEFINITION
PRINCIPLE NTH ROOT

7. DEFINITION
RATIONAL EXPONENTS AND THEIR ROOTS

8. DEFINITION
RADICAL EXPRESSION WITH AN M/N EXPONENT

9. LAWS OF EXPONENTS
If r, s, and t are rational, and a and b are real:

10. LAWS OF EXPONENTS
If r, s, and t are rational, and a and b are real:

11. Chapter 7 Section 7.1A
Practice Test
Exercise #1

12. Find, if possible.

13. Find, if possible.

14. Chapter 7 Section 7.1B
Practice Test
Exercise #4

15. Evaluate if possible.

16. Evaluate, if possible.

17. Section 7.2
Simplifying Radicals

18. OBJECTIVES A
Simplify radical expressions.

19. OBJECTIVES B
Rationalize the denominator of a fraction.

20. OBJECTIVES C
Reduce the order of a radical expression.

21. DEFINITION
nTH ROOT

22. LAWS
For Simplifying Radical
Expressions

23. LAWS
For Simplifying Radical
Expressions

24. LAWS
For Simplifying Radical
Expressions

25. DEFINITION

26. DEFINITION

27. Chapter 7 Section 7.2A
Practice Test
Exercise #7b

28. Simplify.

29. Chapter 7 Section 7.2A
Practice Test
Exercise #8b

30. Simplify.

31. Chapter 7 Section 7.2A
Practice Test
Exercise #9b

32. Simplify.

33. Section 7.3
Operations with Radicals

34. OBJECTIVES A
Add and subtract similar radical expressions.

35. OBJECTIVES B
Multiply and divide radical expressions.

36. OBJECTIVES C
Rationalize the denominators of radical expressions involving sums or differences.

37. DEFINITION LIKE RADICAL EXPRESSIONS
Radical expressions with the same index and the same radicand.

38. DEFINITION
CONJUGATE
The expressions a + b and a – b are conjugates of each other.

39. Chapter 7 Section 7.3A
Practice Test
Exercise #14

40. Perform the indicated operations.

41. Perform the indicated operations.

42. Chapter 7 Section 7.3B
Practice Test
Exercise #16b

43. Perform the indicated operations.

44. Chapter 7 Section 7.3B
Practice Test
Exercise #18b

45. Find the product.

46. Chapter 7 Section 7.3C
Practice Test
Exercise #20

47. Rationalize the denominator.

48. Section 7.4
Solving Equations Containing Radicals

49. OBJECTIVES A
Solve equations involving radicals.

50. OBJECTIVES B
Solve applications requiring the solution of radical equations.

51. DEFINITION
POWER RULE OF EQUATIONS

52. PROCEDURE TO SOLVE EQUATIONS CONTAINING RADICALS Isolate Repeat Raise
Simplify
Check

53. Chapter 7 Section 7.4A
Practice Test
Exercise #21

54. Solve.
When solving by squaring both sides:
x + 2 = 4
x = 2
However, the solution x = does not check.

55. Solve. or

56. Solve.

57. Chapter 7 Section 7.4A
Practice Test
Exercise #22

58. Solve.

59. Solve. or

60. Solve.

61. Section 7.5
Complex Numbers

62. OBJECTIVES Write the square root of a negative integer in terms of i.

63. OBJECTIVES B
Add and subtract complex numbers.

64. OBJECTIVES C
Multiply and divide complex numbers.

65. OBJECTIVES D
Find powers of i.

66. If a and b are real numbers, the following is a complex number:
DEFINITION
COMPLEX NUMBER
If a and b are real numbers, the following is a complex number:

67. RULES
ADDING AND SUBTRACTING COMPLEX NUMBERS

68. PROCEDURE DIVIDING ONE COMPLEX NUMBER BY ANOTHER
Multiply the numerator and the denominator by the conjugate of the denominator.

69. Chapter 7 Section 7.5A
Practice Test
Exercise #26b

70. Write in terms of i.

71. Chapter 7 Section 7.5B
Practice Test
Exercise #27b

72. Find.

73. Chapter 7 Section 7.5C
Practice Test
Exercise #29b

74. Find.

75. Find.

76. Find.

77. Chapter 7 Section 7.5D
Practice Test
Exercise #30b

78. Write the answer as 1, -1, i or -i.