C Challenge

Simplify each radical expression if n is even, and then if n is odd.

49. m n n the th , root of m to the n end root ,
50. m 2 n n the th , root of m super 2 n end super end root ,
51. m 3 n n the th , root of m super 3 n end super end root ,
52. m 4 n n the th , root of m super 4 n end super end root ,
53. Reasoning How many square roots of integers are in the interval between 24 and 25?
54. Reasoning The square root of a positive integer is either a positive integer or an irrational number. Is this a true statement or not? Explain your reasoning.
55. Geometry Without using a calculator, determine which is greater: the altitude of an equilateral triangle with side 8 or the diagonal of a square with side 5. Show your work.

Standardized Test Prep

SAT/ACT

56. Which equation has more than one real-number solution?
    1. x 2 = 0 x squared , equals 0
    2. x 2 = 1 x squared , equals 1
    3. x 2 = − 1 x squared , equals negative 1
    4. x 3 = − 1 x cubed , equals negative 1
57. According to the Rational Root Theorem, which of the following is NOT a possible root of the polynomial equation 7 x 5 + 3 x 2 − 4 x + 21 = 0 ? 7 x to the fifth , plus , 3 x squared , minus 4 x plus 21 equals 0 question mark
    6. 1 7 1 seventh
    7. 1 3 1 third
    8. 3
    9. 7
58. The fuse of a three-break firework rocket is programmed to ignite three times with 2-second intervals between the ignitions. When the rocket is shot vertically in the air, its height h in feet after t seconds is given by the formula h ( t ) = − 5 t 2 + 70 t . h open t close equals negative 5 , t squared , plus 70 t .  At how many seconds after the shot should the firework technician set the timer of the first ignition to make the second ignition occur when the rocket is at its highest point?
    1. 3
    2. 9
    3. 5
    4. 7

    Extended Response

59. Write a system of equations to find a cubic polynomial that goes through ( − 2 , − 35 ) , open negative 2 comma negative 35 close comma  (0, 1), (2, 3), and (4, 7).

Mixed Review

See Lesson 5-9.

Determine the cubic function that is obtained from the parent function y = x 3 y equals , x cubed  after each sequence of transformations.

60. translation up 3 units and to the left 2 units
61. vertical compression by a factor of 1 2 , 1 half , comma  translation down 2 units

See Lesson 4-7.

Solve each equation by using the Quadratic Formula.

62. − 4 x 2 + 7 x − 3 = 0 negative 4 , x squared , plus 7 x minus 3 equals 0
63. 3 x 2 − 5 x + 3 = 0 3 x squared , minus 5 x plus 3 equals 0
64. 36 x 2 − 132 x + 121 = 0 36 x squared , minus 132 x plus 121 equals 0

Get Ready! To prepare for Lesson 6-2, do Exercises 65–67.

See Lesson 1-3.

Simplify each algebraic expression.

65. 14 x 7 y 9 7 x 4 y 6 fraction 14 , x to the seventh , y to the ninth , over 7 , x to the fourth , y to the sixth end fraction
66. 3 a b c 9 b fraction 3 eh b c , over 9 b end fraction
67. 20 x 5 x 3 fraction 20 x , over 5 , x cubed end fraction

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