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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