1. Section 9.1 Finding Roots

2. OBJECTIVES Find the square root of a number. A Square a radical expression. B

3. OBJECTIVES Classify the square root of a number and approximate it with a calculator. C

4. OBJECTIVES Find higher roots of numbers. D Solve an application involving square roots. E

5. DEFINITION If a is a positive real number, Square Root

6. DEFINITION Square Root

7. When the square root of a non- negative real number a is squared, the result is that positive real number: RULE Squaring a Square Root

8. RULE Square Root of a Negative Number

9. Section 9.1 Exercise #1 Chapter 9 Roots and Radicals

10. Find.

11. Section 9.1 Exercise #2 Chapter 9 Roots and Radicals

12. Find the square of each radical expression.

13. Section 9.1 Exercise #3 Chapter 9 Roots and Radicals

14. Classify each number as rational, irrational, or not a real number, and simplify if possible.

15. Section 9.1 Exercise #4 Chapter 9 Roots and Radicals

16. Find each root, if possible.

17. Section 9.1 Exercise #5 Chapter 9 Roots and Radicals

18. The diver takes 2 seconds. A diver jumps from a cliff 20 meters high. If the time t (in seconds) it takes an object dropped from a distance d (in meters) to reach the ground is given by: How long does it take the diver to reach the water?

19. Section 9.2 Multiplication and Division of Radicals

20. OBJECTIVES Multiply and simplify radicals using the product rule. A

21. OBJECTIVES Divide and simplify radicals using the quotient rule. B

22. OBJECTIVES Simplify radicals involving variables. C

23. OBJECTIVES Simplify higher roots. D

24. If a and b are nonnegative numbers, Product Rule for Radicals

25. If a and b are positive numbers, Quotient Rule for Radicals

26. For any real number a, Absolute Value for Radicals

27. For all real numbers where the indicated roots exist, Properties of Radicals

28. Section 9.2 Exercise #6 Chapter 9 Roots and Radicals

29. Simplify.

30. Section 9.2 Exercise #7 Chapter 9 Roots and Radicals

31. Multiply.

32. Section 9.2 Exercise #8 Chapter 9 Roots and Radicals

33. Simplify.

34. Section 9.2 Exercise #9 Chapter 9 Roots and Radicals

35. Simplify.

36. Section 9.2 Exercise #10 Chapter 9 Roots and Radicals

37. Simplify.

38. Section 9.3 Addition and Subtractions of Radicals

39. OBJECTIVES Add and subtract like radicals. A

40. OBJECTIVES Use the distributive property to simplify radicals. B

41. OBJECTIVES Rationalize the denominator in an expression. C

42. Rationalizing Denominators PROCEDURE Method 1: Multiply both numerator and denominator of the fraction by the square root in the denominator.

43. Rationalizing Denominators PROCEDURE Method 2: Multiply numerator and denominator by the square root of a number that makes the denominator the square root of a perfect square.

44. Section 9.3 Exercise #11 Chapter 9 Roots and Radicals

45. Simplify.

46. Section 9.3 Exercise #12 Chapter 9 Roots and Radicals

47. Simplify.

48. Section 9.3 Exercise #13 Chapter 9 Roots and Radicals

49. Simplify.

50. Section 9.3 Exercise #14 Chapter 9 Roots and Radicals

52. Section 9.3 Exercise #15 Chapter 9 Roots and Radicals

54. Section 9.4 Simplifying Radicals

55. OBJECTIVES Simplify a radical expression involving products, quotients, sums, or differences. A

56. OBJECTIVES Use the conjugate of a number to rationalize the denominator of an expression. B

57. OBJECTIVES Reduce a fraction involving a radical by factoring. C

58. Simplifying Radical Expressions RULES 1. Whenever possible, write the rational-number representation of a radical expression.

59. Simplifying Radical Expressions RULES

60. Simplifying Radical Expressions RULES

61. Section 9.4 Exercise #16 Chapter 9 Roots and Radicals

62. Simplify.

64. Section 9.4 Exercise #17 Chapter 9 Roots and Radicals

65. Simplify.

66. Section 9.4 Exercise #18 Chapter 9 Roots and Radicals

67. Simplify.

68. Section 9.4 Exercise #19 Chapter 9 Roots and Radicals

69. Simplify.

70. Section 9.4 Exercise #20 Chapter 9 Roots and Radicals

71. Simplify.

72. Section 9.5 Applications

73. OBJECTIVES Solve equations with one square root term containing the variable. A

74. OBJECTIVES Solve equations with two square root terms containing the variable. B

75. OBJECTIVES Solve an application. C

76. Raising Both Sides of an Equation to a Power PROCEDURE

77. Solving Radical Equations PROCEDURE 1. Isolate the square root term containing the variable. 2. Square both sides of the equation.

78. Solving Radical Equations PROCEDURE 3. Simplify and repeat steps 1 and 2 if there is a square root term containing the variable.

79. Solving Radical Equations PROCEDURE 4. Solve the resulting linear or quadratic equation. 5. Check all proposed solutions in the original equation.

80. Section 9.5 Exercise #22 Chapter 9 Roots and Radicals

81. Solve.

83. Section 9.5 Exercise #23 Chapter 9 Roots and Radicals

84. Solve.

85. Section 9.5 Exercise #24 Chapter 9 Roots and Radicals

86. Solve.