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Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 (For help, go to Lessons 1-2 and 8-5.) Simplify each expression. 1. 112 2. (–12)2 3. –(12)2 4. 1.52 5. 0.62 6. 1 2 7. 2 2 8. 4 2 2 –3 5 10-3 Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 Solutions 1. 112 = 11 • 11 = 121 2. (–12)2 = (–12)(–12) = 144 3. (–12)2 = –(12)(12) = –144 4. 1.52 = (1.5)(1.5) = 2.25 2 5. 0.62 = (0.6)(0.6) = 0.36 6. 1 = 1• 1 = 1 2 2 2 4 2 2 7. – 2 = –2 2 –3 = 4 8. 4 = 4 • 4 = 16 3 3 9 5 5 5 25 10-3 10.3: Finding and estimating Vocabulary: square roots Square root: A number a is a square root of b if a2 = b Radicand: The number inside of the radical sign. The index gives the degree of the root. It is Index: the small number in the “hook” of the radical sign. Principal Root: When a number has two roots, the principle root is the positive root. Property of Square Roots: a a 2 Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 Simplify each expression. a. 25 = 5 positive square root 9 3 3 3 b. ± = ±5 The square roots are and – . 25 5 5 c. – 64 = –8 negative square root d. –49 is undefined For real numbers, the square root of a negative number is undefined. e. ± 0= 0 There is only one square root of 0. 10-3 Rational: Irrational: A number that can be A number that canNOT be written in RATIO form. written as a RATIO. Tell whether each expression is rational or irrational. a. ± 144 = ± 12 rational 1 b. – 5 = –0.44721359 . . . irrational c. – 6.25 = –2.5 rational 1 d. = 0.3 rational 9 e. 7 = 2.64575131 . . . irrational 10-3 Table of Perfect Squares: page 750 N N2 N N2 1 1 9 81 2 4 10 100 3 9 11 121 4 16 13 169 5 25 14 196 6 36 15 225 7 49 16 256 8 64 17 289 N N2 1 1 2 4 3 9 4 16 5 25 6 36 Between what two consecutive integers is 28.34 ? 7 49 8 64 28.34 is between the two consecutive 25 < 28.34 < 36 perfect squares 25 and 36. The square roots of 25 and 36 are 5 and 5< 28.34 < 6 6, respectively. 28.34 is between 5 and 6. 10-3 Find 28.34 to the nearest hundredth. 28.34 5.323532662 Use a calculator. 5.32 Round to the nearest hundredth. 10-3 Suppose a rectangular field has a length three times its width x. The formula d = x2 + (3x)2 gives the distance of the diagonal of a rectangle. Find the distance of the diagonal across the field if x = 8 ft. d= x2 + (3x)2 d= 82 + (3 • 8)2 Substitute 8 for x. d= 64 + 576 Simplify. d= 640 d 25.3 Use a calculator. Round to the nearest tenth. The diagonal is about 25.3 ft long. 10-3 Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 1. Simplify each expression. 4 2 a. 196 14 b. ± ±5 25 2. Tell whether each expression is rational, irrational, or undefined. a. ± 3 b. –25 c. – 2.25 5 irrational undefined rational 3. Between what two consecutive integers is – 54? –8 and –7 4. The formula s = 13.5d estimates the speed s in miles per hour that a car was traveling, when it applied its brakes and left a skid mark d feet long on a wet road. Estimate the speed of a car that left a 120 foot long skid mark. about 40.25 mph 10-3 Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 pages 526–528 Exercises 12. ± 0.1 24. –12.25 1. 13 13. irrational 25. 0.93 2. 20 14. rational 26. ± 20 3. 1 15. irrational 27. 0 3 4. 30 16. rational 28. ± 25 5. 0.5 17. 5 and 6 29. ±3 7 6. 6 18. 5 and 6 30. ± 1.3 7 7. –1.1 19. –12 and –11 31. ±1 9 8. 1.4 20. 13 and 14 32. ± 27 9. 0.6 21. 3.46 33. ± 1.5 10. –12 22. –14.25 34. ± 16 11. 5 23. 107.47 35. ± 0.1 4 10-3 Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 36. ± 8 47. 6.40 54. false; 1=1 11 37. ± 202 48. 8.66 55. true 38. 1 49. Answers may vary. Sample: 56. true The first expression means 57. False; answers may vary. 39. a. 8450 km the neg. square root of 1 and b. 7684 km Sample: 4 + 9 = 4 + 9. / the second expression means 40. 21 the pos. square root of 1. 58. False; answers may vary. 50. Answers may vary. Sample: 12 and 3 are 41. – 2 irrational but 36 is rational. 5 Sample: 3 and 4 42. 1.41 59. a. 4 units2 51. 4 43. 1.26 52. a. 5 s b. 1 unit2 2 44. –5.48 b. 10 s c. 2 units2 c. No; the object takes 45. –33 twice as long to fall. d. 2 units 46. –0.8 53. False; zero has one square root. 10-3 Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 60. 1.3 67. 70. 61. 6 62. 2 9 63. 9 64. 11 68. 71. 65. 128 66. 69. 72. d 2 – 81 73. 9t 2 – 25 74. 8075 10-3 Finding and Estimating Square Roots ALGEBRA 1 LESSON 10-3 75. x2 + 26x + 169 76. 16y2 – 56y + 49 77. 10,201 78. 813,604 79. 36k2 – 49 80. 144b2 – 168b + 49 81. –2 82. 3 16 83. – 3 4 84. –972 85. 1 12 86. 81 4 10-3

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posted: | 5/24/2012 |

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