Operations with Radical Expressions

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Presentation transcript:

Operations with Radical Expressions ALGEBRA 1 LESSON 11-4 pages 603–606 Exercises 1. 5 6 2. 18 10 3. –2 5 4. 2 7 5. 14 2 6. –8 3 7. yes 8. yes 9. no 10. 4 2 11. –3 3 12. 4 2 13. –2 5 14. 7 15. 8 10 16. 4 – 4 2 17. 9 + 3 18. 6 – 2 3 19. 3 5 + 2 3 20. 3 2 + 6 21. 6 – 5 6 22. –9 – 14 6 23. 58 – 10 30 24. 11 – 4 7 25. 43 + 4 30 26. 32 + 9 11 27. 23 – 5 13 28. 2 7 + 2 3 29. –6 2 30. –4 6 – 12 2 31. 32. –5 11 – 5 3 33. 18 3 + 9 11 34. 10 2 + 10; 24.1 3( 10 + 5) 5 11-4

Operations with Radical Expressions ALGEBRA 1 LESSON 11-4 46. 4 3 + 4 2 + 3 6 + 6 47. 48. 8 2 units 49. 10 + 10 2 units 50. 6 10 units 51. 4x + x 10 units 52. Answers may vary. Sample: 8 2 + 4 3, 2 7 + 9 3, 6 5 + 3 7 53. a. The student simplified 48 as 2 24 instead of 2 12 or 4 3. b. 2 6 + 4 3 54. a. 2 2 or 2.8 ft b. s 2 35. – ; –1.3 36. 6 – 4 2; 0.3 37. 7.4 ft 38. 5 10 39. 6 2 + 6 3 40. 22 3 – 6 41. 8 + 2 15 42. 43. 15 + 4 14 44. –24 45. – 2 4 3 10 5 13 + 65 + 130 + 5 2 8 11-4

Operations with Radical Expressions ALGEBRA 1 LESSON 11-4 55. 9.1% 56. 12.8% 57. 15.5% 58. a. x b. x x 59. 60. about 251 years 61. They are unlike radicals. 62. a. 1, 0, 1, 1; 4, 1, 5, 17; 5, 3, 8, 34; 8, 6, 14, 10; 10, 9, 19, 181 b. No; the only values it worked for were 0 and 1. 63. a + b = a + b 64. 65. 66. 67. 2 68. 10 2 69. 70 70. 2 2 – 6 – 3 + 3 71. a. 2 6 b. 2 13 c. 2(p + q) 72. B / 9 2 2 23 7 21 n 2 n – 1 2 8 15 15 ab b 11-4

Operations with Radical Expressions ALGEBRA 1 LESSON 11-4 73. I 74. [2] (3 5 – 2)( 5 + 5 2) = 3 25 + 15 10 – 10 – 5 4 = 3(5) + 15 10 – 10 – 5(2) = 15 + 15 10 – 10 – 10 = 5 + 14 10 [1] correct technique, but with a computational error 75. [4] [3] correct steps but answer not completely simplified [2] correct technique, but with a computational error [1] correct answer but no work shown 7 – 21 5 7 + 21 • Multiply the numerator and denominator by the conjugate of the denominator. Simplify the denominator. 11-4

Operations with Radical Expressions ALGEBRA 1 LESSON 11-4 76. 9.2 units 77. 6.7 units 78. 26.2 units 79. (3, 5) 80. (–2, 6.5) 81. 0, 7 82. –2, 9 83. –9, –3 84. –4, 6 85. –15, –2 86. –3, – 87. b2 + 22b + 121 88. 4p2 + 28p + 49 89. 25g2 – 49 90. 9x2 – 1 91. k2 – 81 92. d 2 – 2.2d + 1.21 1 9 1 2 11-4