PRE-AP ALGEBRA II

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```					Pre AP Alg II                                                              Name                             ______
Ch 6 Review                                                                Date                      Pd

Find all the real square roots of each number.

16
1. 625                                                           2.
81

Find all the real cube roots of each number.

1
3. –216                                    4.                                     5. 0.027
64
Find all the real fourth roots of each number.

6. 0.2401                                                        7. 1

Find each real root.

8.    400                                  9.  4 256                                    10.   3
729

Simplify each radical expression.

11.       25x 6                            12.   3
343x9 y12                           13. 4 16x16 y 20

4
15. The formula for the volume of a sphere is V   r 3 . Solving for r, the radius of
3
3V
a sphere is r  3      . If the volume of a sphere is 20 ft3, what is the radius of the sphere
4
to the nearest hundredth?

Find the two real solutions of each equation.

2401
16. x4  81                                17. x2  144                                  18. x 4 
625

Multiply, if possible. Then simplify.

19.   3
43 6                            20.       5 8                                21.   3
64 9
Simplify.

3
22.       27x 6                      23.       48x3 y 4                     24. 5 128x2 y 25

Multiply and simplify. Assume all variables are positive.

25. 12  3                           26.   4
7 x 6  4 32 x 2             27. 2 3 6 x4 y  3 3 9 x5 y 2

Simplify each expression. Assume all variables are positive.

28.   3
4  3 80                   29. 5 2 xy6  2 2 x3 y                 30. 5               5  15   

Divide and simplify. Assume all variables are positive.

36 x 6                           4
405 x8 y 2                   3
75 x7 y 2
31.                                  32.                              33.
9x 4                                4
5 x3 y 2                     4
25 x 4

Rationalize the denominator of each quotient. Assume all variables are positive.

26                               3
x                                        7 x4 y
35.                                  36.   3
37.
3                                   2                                         5 xy

38. Einstein’s famous formula E = mc2 relates energy E, mass m, and the speed of light c.
Solve the formula for c. Rationalize the denominator.
39. The formula h = 16t2 is used to measure the time t it takes for an object to free fall from
height h. If an object falls from a height of h = 18a5 ft, how long did it take for the object
in terms of a?

Simplify if possible.

40. 3 5  4 5                          41. 8 3 4  6 3 4                       42. 2 xy  2 y

Simplify.

43. 18  32                            44. 4 324  4 2500                      45. 3 192  3 24

Multiply.

       
46. 3  6 2  6                                   
47. 5  5 1  5                        48.  4  7 
2

Multiply each pair of conjugates.

       
49. 7  2 7  2                                    
50. 1  3 3 1  3 3                         
51. 6  4 7 6  4 7    

Rationalize each denominator. Simplify the answer.

3                                  7 5                                    1  2 10
52.                                    53.                                     54.
2 6                                   6 5                                    4  10
Simplify. Assume that all variables are positive.

55.       45  80  245                   
56. 2  98 3  18                             57. 6 192 xy 2  4 3xy 2

Simplify each expression.

1                                           1            1       1                1       1
58. 16 4                            59. (3) 3  (3) 3  (3) 3                      60. 5 2  45 2

Write each expression in radical form.

1                                   4                                                 2
61. x 4                             62. x 5                                           63. x 9

Write each expression in exponential form.

3
64.   3
2                         65.        2x 2                                   66.   3
(2 x)2

Simplify each number.
1
67. (216) 3                        68. 2431.2                                        69. 32 − 0.4

Find each product or quotient.

  
5
x2
70.       4
6       3
6         71.                                              72.        20  3 135
10          2
x

Simplify each number.

2                                           2            2                        2
73. (125) 3                         74. (216) 3 (216) 3                            75. (243) 5
Write each expression in simplest form. Assume that all variables are positive.
1
3                                      1
 x2 3
76. 16x     
8 4
77.  8x   
15  3
78.  10 
x 

Solve.

79.   x2 20                          80.   2x  3  7  0                    81. 2  3x  2  6

Solve.

2                                       3                                      1
82. 2( x  2) 3  50                    83. 2( x  3) 2  54                    84. (6 x  5) 3  3  2

85. A cylindrical can holds 28 in.3 of soup. If the can is 4 in. tall, what is the radius of the
can to the nearest tenth of an inch? ( Hint : V   r 2 h)

Solve. Check for extraneous solutions.

86.   4x  5  x  2                    87.   3x  5  3  x                   88.   x7 5 x

89.   2x  7  x  2                    90. 3x  2  2 x  7  0                91.   2x  4  2  x

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