Rationalize the denominator in each expression. Assume that all variables represent positive
real numbers. See Examples 2 and 3.
48. 49. 50. 51. 52.
53. 54. 55. 56. 57.
58. 59. 60. 61. 62.
63. 64. 65.
66. 67. 68.
Simplify. Assume that all variables represent positive real numbers. See Example 4.
69. 70. 71. 72. 73.
74. 75. 76. 77. 78.
79. 80. 81. 82.
Rationalize the denominator in each expression. Assume that all variables represent positive
real numbers and no denominators are 0. See Example 5.
86. 87. 88.
89. 90. 91.
92. 93. 94.
95. 96. 97. 98.
Write each expression in lowest terms. Assume that all variables represent positive real
numbers. See Example 6.
99. 100. 101. 102.
103. 104. 105. 106.
11 y- 2242 y^5
22 y6 p+ 224 p^3
3 p12 - 9272
18
16 - 428
12
- 5 + 522
5
3 - 325
3
24 + 1225
12
30 - 2026
10
32 x
2 x- 22 y52 k
22 k+ 2 q2 a+ 2 b
2 a- 2 b2 x- 2 y
2 x+ 2 y5
32 r+ 2 s4
2 x- 22 yr- 9
2 r- 3m- 4
2 m+ 225 + 26
23 - 22
22 - 23
26 - 25
- 1
322 - 227
2
325 + 223
227
3 - 23
28
3 - 22
4
5 + 26
3
4 + 25
B
4
7 t
B s^24
2 y
B z4
81
B y4
16
xB
3
m^9
B q3
x^6
y-
B
3
6 x
y^2-
B
3
2 p
B r^23
10
9
B
3
9
B^32
3
5
B^16
3
4
B^9
3
4
B^5
3
2
3
-
B
75 m^3
p-
B
48 k^2
z225 r
2 m^3522 m
B 2 y^3242 t^9
B u^11288 x^7
y^9-
B
98 r^3
s^5-
B
150 m^5
n^3- 4213
2 m- 823
B 2 k52
yB
24
x