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Name:_____________________________ Period:______ Date:______ Algebra 3 Unit 14 – 10.5 – 10.7
I. Rationalize the denominator of the following. Simplify if possible.
1.
2
7
2.
*4.
6
3
9
5.
*7.
3
7 4
*8.
4
3
4
25
y
3.
16
9x 7
*6.
24 x5
3y2
9.
2 3 6
4 3 6
2 3
2 3
3
II. Rationalize the numerator. Simplify if possible.
*10.
*13.
24 x5
3y2
11.
15  1
2
14.
3
5
3
12.
x 5
3
15.
3
5 y2
4x
8 3
2 3
III. Solve the following radical equations. Check for extraneous answers.
16.
x 1  5
17.
19.
x  4  2x  5
x5  4 x6
22.
4
2x  3  2  1
18.
5x  6  1
20.
13  x  x  1
21.
2x  3  3  x
23.
3x  8  3x  4
*24. x  9  2  x  7
3
IV. Find the missing dimension.
25.
26.
7 cm
?
?
6 ft
5 cm
3 ft
27. A spotlight is mounted on the eaves of a house 12 feet above the ground. A flower bed runs between the
house and the sidewalk, so the closest the ladder can be placed to the house is 5 feet. How long a ladder is
needed so that an electrician can reach the place where the light is mounted?
Height of
ladder?
12 ft
5 ft
28. A wire is to be attached to support a telephone pole. Because of surrounding buildings, sidewalks, and
roadways, the wire must be anchored exactly 15 feet from the base of the pole. Telephone company workers
have only 30 feet of cable, and 2 feet of that must be used to attach the cable to the pole and to the stake on
the ground. How high from the base of the pole can the wire be attached?
15 ft
V. Write in terms of i.
29.
49
30.
27
31.  24
32.
15  10
33.
27  12
34.
8
2
VI. Perform the indicated operation. Write your answer in the form
35.
 4  2i    7i 
36.
38. 4i   5i 
41.
 3  2i 
44.
2  3i
2i
3  i    6  5i 
39. 2i  3  5i 
2
42.
 4  3i  4  3i 
45.
7
1  4i
a  bi .
37.
 2  i    3  4i   1  5i 
40.
 6  7i  2  4i 
43.
9
2i
VII. Find the powers of i.
46. i19
47. i 14
48. i 53
49. i100