C Challenge

61. Geometry A square has sides with length n. How much must be added to the length of one side to transform the square into a golden rectangle?
62. Reasoning What are three fractions that you can multiply 1 2 + 3 fraction 1 , over square root of 2 plus 3 end fraction  by to rationalize the denominator? Will the resulting products be the same? Explain.
63. Geometry Find the length of each hypotenuse. Write your answer in simplified radical form.
    1. 
    2. 
    3. 

Standardized Test Prep

SAT/ACT

64. What is the simplified form of 2 18 − 32 + 4 8 ? 2 square root of 18 minus square root of 32 plus 4 square root of 8 question mark
    1. 8 3 8 square root of 3
    2. 10 2 10 square root of 2
    3. 18 2 18 square root of 2
    4. 10 18 10 , square root of 18

65. A surveyor is calculating the areas of lots that are going to be sold.

    The dimensions of one lot are shown below. What is the area of the lot shown?

    

    6. 8.82   ×   10 6   m 2 8.82 , times , 10 to the sixth , , m squared
    7. 8.82   ×   10 5   m 2 8.82 , times , 10 to the fifth , , m squared
    8. 4.41   ×   10 5   m 2 4.41 , times , 10 to the fifth , , m squared
    9. 4.41   ×   10 6   m 2 4.41 , times , 10 to the sixth , , m squared

66. What are the approximate solutions of the equation 5 2 x 2 + 3 4 x − 5 = 0 ? 5 halves , x squared , plus , 3 fourths , x minus 5 equals 0 question mark

    Use a graphing calculator.

    1. − 5 ,   0 negative 5 comma 0
    2. − 1.57 ,   1.27 negative , 1.57 , comma , 1.27
    3. − 1.36 ,   0.71 negative , 1.36 , comma , 0.71
    4. − 0.96 ,   0.84 negative , 0.96 , comma , 0.84

67. Short Response What are the domain and range of the function y = | x | ? y equals absolute value of x , , question mark  Show how you find your answer.

Mixed Review

See Lesson 10-2.

Simplify each radical expression.

68. 108 square root of 108
69. 3 150 3 , square root of 150
70. 4 18 c 2 fraction 4 , over square root of 18 , c squared end root end fraction
71. 5 · 45 square root of 5 middle dot square root of 45

See Lesson 7-3.

Rewrite each expression using each base only once.

72. 8 5 · 8 11 8 to the fifth , middle dot , 8 to the eleventh
73. 2 24 · 2 − 13 2 to the twenty fourth , middle dot , 2 super negative 13 end super
74. 5 11 · 5 16 5 to the eleventh , middle dot , 5 to the sixteenth
75. 3 7 · 3 − 4 3 to the seventh , middle dot , 3 super negative 4 end super

Get Ready! To prepare for Lesson 10-4, do Exercises 76–81.

See Lesson 9-4.

Solve by factoring.

76. x 2   +   2 x   +   1   =   0 x squared , plus 2 x plus 1 equals 0
77. x 2   + x − 12 = 0 x squared , plus x minus 12 equals 0
78. x 2   +   2 x − 15   =   0 x squared , plus 2 x minus 15 equals 0
79. 3 x 2   +   7 x − 6   =   0 3 , x squared , plus 7 x minus 6 equals 0
80. 2 x 2   +   3 x − 2   =   0 2 , x squared , plus 3 x minus 2 equals 0
81. x 2   +   14 x   +   49   =   0 x squared , plus 14 x plus 49 equals 0

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