(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