Express each radical in simplified form. Assume that all variables represent positive real
numbers. See Example 5.
75. 76. 77. 78.
79. 80. 81. 82.
83. 84. 85. 86.
87. 88. 89. 90.
91. 92. 93. 94.
Simplify each radical. Assume that. See Example 6.
Simplify by first writing the radicals as radicals with the same index. Then multiply. Assume
that all variables represent positive real numbers. See Example 7.
Find the unknown length in each right triangle. Simplify the answer if possible. See Example 8.
110. 111. 112.
Find the distance between each pair of points. See Example 9.
- and 114. and
- and 116. and
- and 118. and
- and 120. and
- and 122. and
- 1 x+y, y 2 and 1 x-y, x 2 124. 1 c, c-d 2 and 1 d, c+d 2
A^22 ,^26 B A-^222 , 4^26 B A^27 , 9^23 B A-^27 , 4^23 B
1 4.7, 2.3 2 1 1.7, -1.7 2 1 - 2.9, 18.2 2 1 2.1, 6.2 2
1 - 8, 2 2 1 - 4, 1 2 1 - 1, 2 2 1 5, 3 2
1 - 6, 5 2 1 3, - 42 1 - 1, 5 2 1 - 7, 7 2
1 6, 13 2 1 1, 1 2 1 8, 13 2 1 2, 5 2
257 # 275 2 x# 23 x 23 y# 24 y
234 # 23 235 # 26 243 # 234
268 210 x^25212 x^4424482 24502 2425
xÚ 0B
3
y^17
B 1253
x^16
B 27v^13
B 49y^11
362481 x^12 y^162481 t^8 u^28 - 24162 r^15 s^10 - 2432 k^5 m^10238 z^6 w^92364 a^15 b^1223 - 16 z^5 t^723 - 81 m^4 n^10- 2500 r^11 - 2200 p^13213 x^7 y^8223 k^9 p^14
250 x^32300 z^3
B4
81
256
t^12 u^8
B4
1
16
r^8 t^20- 225 t^6 s^20 - 23 - 125 a^6 b^9 c^12 - 23 - 216 y^15 x^6 z^3
- 2327 t^12 - 2364 y^18 - 2100 m^8 z^4
2169 s^5 t^102121 x^62256 z^12272 k^2218 m^22144 x^3 y^9SECTION 8.3 Simplifying Radical Expressions 451
90 °34c90 °6b9
a590 °9
90 °117a90 °5
c1290 °4
12b