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Algebra Review
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Algebra Review
Simplify the radical expression. 13. 75 + 3. 14. 50 º 18. 15. 64 º 28. 16. 44 + 211. 17. 125 º 80. 18. 242 + 200. 19. º147 º 243. 20. 28 + 63. 21...
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CHAPTER
8
Algebra Review EXAMPLE 1
Simplifying Radicals
Simplify the expression 兹2苶0苶. 兹2苶0苶 = 兹4苶 • 兹5苶 = 2兹5苶
Use product property. Simplify.
EXERCISES Simplify the expression. 1. 兹1 苶2苶1苶
2. 兹5 苶2苶
3. 兹4 苶5苶
4. 兹7 苶2苶
5. 兹4 苶0苶
6. 兹2 苶7苶
7. 兹8 苶0苶
8. 兹5 苶0苶
9. 兹2 苶4苶3苶
10. 兹2 苶8苶8苶
11. 兹3 苶2苶0苶
12. 兹2 苶2苶5苶
EXAMPLE 2
Simplifying Radical Expressions
Simplify the radical expression. a. 5兹3 苶 º 兹3苶 º 兹2苶
= 4兹3苶 º 兹2苶
b. (2兹2 苶)(5兹3苶)
c. (5兹7 苶)2
= 2 • 5 • 兹2苶 • 兹3苶
= 52兹7苶2苶
= 10兹6苶
= 25 • 7 = 175
EXERCISES Simplify the radical expression. 13. 兹7 苶5苶 + 兹3苶
14. 兹5 苶0苶 º 兹1苶8苶
15. 兹6 苶4苶 º 兹2苶8苶
16. 兹4 苶4苶 + 2兹1苶1苶
17. 兹1 苶2苶5苶 º 兹8苶0苶
18. 兹2 苶4苶2苶 + 兹2苶0苶0苶
19. º兹1 苶4苶7苶 º 兹2苶4苶3苶
20. 兹2 苶8苶 + 兹6苶3苶
21. 兹2 苶0苶 + 兹4苶5苶 º 兹5苶
22. (兹1 苶3苶)(兹2苶6苶)
23. (3兹1 苶4苶)(兹3苶5苶)
24. (兹3 苶6苶3苶)(兹3苶0苶0苶)
25. (6兹2 苶)(2兹2苶)
26. (兹1 苶8苶)(兹7苶2苶)
27. (兹2 苶1苶)(兹2苶4苶)
28. (兹3 苶2苶)(兹2苶)
29. (兹9 苶8苶)(兹1苶2苶8苶)
30. (5兹4 苶)(2兹4苶)
31. (6兹5 苶)
32. (4兹2 苶)
33. (8兹3 苶)2
34. (2兹3 苶)2
35. (5兹5 苶)2
36. (10兹1 苶1苶)2
2
522
Chapter 8
2
Page 2 of 2
EXAMPLE 3
Simplifying Quotients with Radicals 6 兹5 苶
Simplify the quotient ᎏ. 6 6 苶 兹5 ᎏ=ᎏ•ᎏ 兹5 苶 兹5 苶 兹5 苶
Multiply numerator and denominator by 兹5苶, to eliminate a radical in the denominator.
6兹5 苶 兹5 苶 兹5 苶 6兹5 苶 =ᎏ 5
=ᎏ
EXERCISES Simplify the quotient.
4 37. ᎏ 兹3 苶
5 38. ᎏ 兹7 苶
2兹3 苶 39. ᎏ 兹6 苶
2兹3 苶 40. ᎏ 兹5 苶
兹1 苶8 苶 41. ᎏ 3兹2 苶
4 42. ᎏ 兹8 苶
16 43. ᎏ 兹2 苶4 苶
苶 兹5 44. ᎏ 兹1 苶0 苶
4 45. ᎏ 兹1 苶2 苶
3兹5 苶 46. ᎏ 兹2 苶0 苶
9 47. ᎏ 兹5 苶2 苶
兹1 苶2 苶 48. ᎏ 兹2 苶4 苶
苶8 苶 兹1 49. ᎏ 兹1 苶0 苶
苶2 苶 兹3 50. ᎏ 兹5 苶
苶7 苶 兹2 51. ᎏ 兹4 苶5 苶
兹5 苶0 苶 52. ᎏ 兹7 苶5 苶
EXAMPLE 4
Solving Quadratic Equations
Solve. x2 º 5 = 16 x2 = 21 x = ±兹2苶1苶
Add 5 to each side. Find square roots.
EXERCISES Solve. 53. x 2 = 9
54. x 2 = 625
55. x 2 = 289
56. x 2 + 3 = 13
57. x 2 º 4 = 12
58. x 2 º 7 = 6
59. 7x 2 = 252
60. 3x 2 = 192
61. 6x 2 = 294
62. 4x 2 + 5 = 45
63. 2x 2 + 5 = 23
64. 9x 2 + 7 = 52
65. 11x2 + 4 = 48
66. 6x2 º 3 = 9
67. 10x2 º 16 = º6
68. 5x 2 º 6 = 29
69. 8x2 º 12 = 36
70. 5x 2 º 61 = 64
71. x2 + 32 = 52
72. 72 + x 2 = 252
73. 52 + 122 = x2
Algebra Review
523
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