This is “Review Exercises and Sample Exam”, section 8.7 from the book Beginning Algebra (v. 1.0). For details on it (including licensing), click here.
For more information on the source of this book, or why it is available for free, please see the project's home page. You can browse or download additional books there. To download a .zip file containing this book to use offline, simply click here.
(Assume all variables represent nonnegative numbers.)
Radicals
Simplify.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Simplifying Radical Expressions
Simplify.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Use the distance formula to calculate the distance between the given two points.
25. (5, −8) and (2, −10)
26. (−7, −1) and (−6, 1)
27. (−10, −1) and (0, −5)
28. (5, −1) and (−2, −2)
Adding and Subtracting Radical Expressions
Simplify.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
Multiplying and Dividing Radical Expressions
Multiply.
45.
46.
47.
48.
49.
50.
51.
52.
Divide.
53.
54.
55.
56.
Rationalize the denominator.
57.
58.
59.
60.
61.
62.
63.
64.
Rational Exponents
Express in radical form.
65.
66.
67.
68.
Write as a radical and then simplify.
69.
70.
71.
72.
73.
74.
Perform the operations and simplify. Leave answers in exponential form.
75.
76.
77.
78.
79.
80.
81.
82.
Solving Radical Equations
Solve.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
In problems 1–18, assume all variables represent nonnegative numbers.
1. Simplify.
2. Simplify.
3.
4.
5.
6.
Perform the operations.
7.
8.
9.
10.
Rationalize the denominator.
11.
12.
13.
14.
Perform the operations and simplify. Leave answers in exponential form.
15.
16.
17.
18.
Solve.
19.
20.
21.
22.
23.
24.
25. The period, T, of a pendulum in seconds is given the formula , where L represents the length in feet. Calculate the length of a pendulum if the period is 1½ seconds. Round off to the nearest tenth.
1: 6
3: Not a real number
5:
7: 1/4
9:
11:
13:
15:
17:
19:
21:
23:
25:
27:
29:
31:
33:
35:
37:
39:
41:
43:
45:
47:
49: −4
51:
53:
55:
57:
59:
61:
63:
65:
67:
69: 2
71:
73: 1/8
75: 9
77: 4
79:
81:
83: 25
85: 17
87: 6
89: 8
91: −1/2, −1
93: 2/3, −4
95: −5, 5/3
97: 9
99: 9
1:
3:
5:
7:
9:
11:
13:
15:
17:
19: 49
21: 5
23: −1/2, 1/3
25: 1.8 feet