Section 9.1Properties of Radicals 487In Exercises 65–68, evaluate the function for the given value of x. Write your answer in simplest form and in decimal form rounded to the nearest hundredth.65. h(x) √— 5x ; x 10 66. g(x) √— 3x ; x 60 67. r(x) — 3x — 3x2 + 6 ; x 4 68. p(x) — x 1 — 5x ; x 8In Exercises 69–72, evaluate the expression when a= −2, b= 8, and c = 1 — 2 . Write your answer in simplest form and in decimal form rounded to the nearest hundredth.69. √— a2 + bc 70. √— 4c 6ab 71. √— 2a2 + b2 72. √— b2 4ac 73. MODELING WITH MATHEMATICS The text in the book shown forms a golden rectangle. What is the width w of the text? (See Example 7.)6 in.w in. 74. MODELING WITH MATHEMATICS The ag of Togo is approximately the shape of a golden rectangle. What is the width w of the ag?42 in.w in.In Exercises 75–82, simplify the expression. (See Example 8.)75. √— 3 2 √— 2 + 6 √— 2 76. √— 5 5 √— 13 8 √— 5 77. 2 √— 6 5 √— 54 78. 9 √— 32 + √— 2 79. √— 12 + 6 √— 3 + 2 √— 6 80. 3 √— 7 5 √— 14 + 2 √— 28 81. 3 √— 81 + 4 3 √— 3 82. 6 3 √— 128t 2 3 √— 2t In Exercises 83–90, simplify the expression. (See Example 9.)83. √— 2 ( √— 45 + √— 5 ) 84. √— 3 ( √— 72 3 √— 2 ) 85. √— 5 ( 2 √— 6x √— 96x ) 86. √— 7y ( √— 27y + 5 √— 12y ) 87. ( 4 √— 2 √— 98 ) 2 88. ( √— 3 + √— 48 ) ( √— 20 √— 5 ) 89. 3 √— 3 ( 3 √— 4 + 3 √— 32 ) 90. 3 — 2 ( 3 √— 135 4 3 √— 5 ) 91. MODELING WITH MATHEMATICS The circumference C of the art room in a mansion is approximated by the formula C ≈ 2π — a2 + b2 — 2. Approximate the circumference of the room.diningroomlivingroomentrancehallhallguestroomguestroomenentntnttrrarancehalla = 20 ftb = 16 ft 92. CRITICAL THINKING Determine whether each expression represents a rational or an irrational number. Justify your answer. a. 4 + √— 6 b. √— 48 — √— 3 c. 8 — √— 12 d. √— 3 + √— 7 e. a —
√— 10 √— 2 , where a is a positive integer f. 2 + √— 5 —
2b + √— 5b2 , where b is a positive integerIn Exercises 93–98, simplify the expression. 93. 5 — 13 — 5x5 94. 4 — 10 — 81 95. 4 √— 256y 96. 5 √— 160x6 97. 6 4 √— 9 5 √— 9 + 3 4 √— 9 98. 5 √— 2 ( 4 √— 7 + 5 √— 16 )