Chapter 9: Exercises with Answers

942 Chapter 9 Radical Functions
34. − √ 20 + 4 √ 45
35. −5 √ 27 + 5 √ 12
36. 3 √ 12 − 2 √ 27
37. 4 √ 20 + 4 √ 45
38. −2 √ 18 − 5 √ 8
39. 2 √ 45 + 5 √ 20
40. 3 √ 27 − 4 √ 12
In Exercises 41-48, simplify each of the
given rational expressions. Place your final
answer in simple radical form. Check
your result with your calculator.
41.
√
2 −
1 √2
42. 3 √ 3 − 3 √
3
43. 2 √ 2 − 2 √
2
44. 4 √ 5 − 5 √
5
45. 5 √ 2 + 3 √
2
46. 6 √ 3 + 2 √
3
47.
48.
√
8 −
12
√
2
− 3 √ 2
√
27 −
6 √3 − 5 √ 3
In Exercises 49-60, multiply to expand
each of the given radical expressions. Place
your final answer in simple radical form.
Use your calculator to check your result.
49. (2 + √ 3)(3 − √ 3)
50. (5 + √ 2)(2 − √ 2)
51. (4 + 3 √ 2)(2 − 5 √ 2)
52. (3 + 5 √ 3)(1 − 2 √ 3)
53. (2 + 3 √ 2)(2 − 3 √ 2)
54. (3 + 2 √ 5)(3 − 2 √ 5)
55. (2 √ 3 + 3 √ 2)(2 √ 3 − 3 √ 2)
56. (8 √ 2 + √ 5)(8 √ 2 − √ 5)
57. (2 + √ 5) 2
58. (3 − √ 2) 2
59. ( √ 3 − 2 √ 5) 2
60. (2 √ 3 + 3 √ 2) 2
In Exercises 61-68, place each of the
given rational expressions in simple radical
form by “rationalizing the denominator.”
Check your result with your calculator.
61.
62.
63.
1
√
5 +
√
3
1
2 √ 3 − √ 2
6
2 √ 5 − √ 2
64.
9
3 √ 3 − √ 6
Version: Fall 2007