Chapter 9: Exercises with Answers

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902 Chapter 9 Radical Functions 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. √ 16h 8 √ 25f 2 √ 25j 8 √ 16m 2 √ 25a 2 √ (7x + 5) 12 √ 9w 10 √ 25x 2 − 50x + 25 √ 49x 2 − 42x + 9 √ 25x 2 + 90x + 81 √ 25f 14 √ (3x + 6) 12 √ (9x − 8) 12 for x = −2. 49. Given that x < 0, place the radical expression √ 27x 12 in simple radical form. Check your solution on your calculator for x = −2. 50. Given that x < 0, place the radical expression √ 44x 10 in simple radical form. Check your solution on your calculator for x = −2. In Exercises 51-54, follow the lead of Example 17 in the narrative to simplify the given radical expression and check your result with your graphing calculator. 51. Given that x < 4, place the radical expression √ x 2 − 8x + 16 in simple radical form. Use a graphing calculator to show that the graphs of the original expression and your simple radical form agree for all values of x such that x < 4. 41. 42. 43. 44. 45. 46. √ 36x 2 + 36x + 9 √ 4e 2 √ 4p 10 √ 25x 12 √ 25q 6 √ 16h 12 47. Given that x < 0, place the radical expression √ 32x 6 in simple radical form. Check your solution on your calculator for x = −2. 48. Given that x < 0, place the radical expression √ 54x 8 in simple radical form. Check your solution on your calculator 52. Given that x ≥ −2, place the radical expression √ x 2 + 4x + 4 in simple radical form. Use a graphing calculator to show that the graphs of the original expression and your simple radical form agree for all values of x such that x ≥ −2. 53. Given that x ≥ 5, place the radical expression √ x 2 − 10x + 25 in simple radical form. Use a graphing calculator to show that the graphs of the original expression and your simple radical form agree for all values of x such that x ≥ 5. 54. Given that x < −1, place the radical expression √ x 2 + 2x + 1 in simple radical form. Use a graphing calculator to show that the graphs of the original expression and your simple radical form agree for all values of x such that x < −1. Version: Fall 2007
Section 9.2 Multiplication Properties of Radicals 903 In Exercises 55-72, place each radical expression in simple radical form. Assume that all variables represent positive numbers. In Exercises 73-80, place each given radical expression in simple radical form. Assume that all variables represent positive numbers. 55. √ 9d 13 73. √ 2f 5 √ 8f 3 56. √ 4k 2 74. √ 3s 3 √ 243s 3 57. √ 25x 2 + 40x + 16 75. √ 2k 7 √ 32k 3 58. √ 9x 2 − 30x + 25 76. √ 2n 9 √ 8n 3 59. √ 4j 11 77. √ 2e 9 √ 8e 3 60. √ 16j 6 78. √ 5n 9 √ 125n 3 61. √ 25m 2 79. √ 3z 5 √ 27z 3 62. √ 9e 9 80. √ 3t 7 √ 27t 3 63. √ 4c 5 64. √ 25z 2 65. √ 25h 10 66. √ 25b 2 67. √ 9s 7 68. √ 9e 7 69. √ 4p 8 70. √ 9d 15 71. √ 9q 10 72. √ 4w 7 Version: Fall 2007
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Chapter 9: Exercises with Answers

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