Download Exercises with Answers

Section 9.2
Multiplication Properties of Radicals
901
9.2 Exercises
1.
√ √Use a calculator to first approximate
√5 2. On the same screen, approximate
10. Report the results on your homework paper.
14.
15.
16.
2.
√ √Use a calculator to first approximate
7 10.
√ On the same screen, approximate 70. Report the results on your
homework paper.
3.
√ √Use a calculator to first approximate
3 11.
√ On the same screen, approximate 33. Report the results on your
homework paper.
4.
√ √Use a calculator to first approximate
5 13.
√ On the same screen, approximate 65. Report the results on your
homework paper.
In Exercises 5-20, place each of the radical expressions in simple radical form.
As in Example 3 in the narrative, check
your result with your calculator.
√
5.
18
√
6.
80
√
7.
112
√
8.
72
√
9.
108
√
10.
54
√
11.
50
√
12.
48
√
13.
245
1
17.
18.
19.
20.
√
√
√
√
√
√
√
150
98
252
45
294
24
32
In Exercises 21-26, use prime factorization (as in Examples 10 and 11 in the
narrative) to assist you in placing the
given radical expression in simple radical form. Check your result with your
calculator.
√
21.
2016
√
22.
2700
√
23.
14175
√
24.
44000
√
25.
20250
√
26.
3564
In Exercises 27-46, place each of the
given radical expressions in simple radical form. Make no assumptions about
the sign of the variables. Variables can
either represent positive or negative numbers.
p
27.
(6x − 11)4
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Version: Fall 2007
902
Chapter 9
√
29.
16h8
p
25f 2
30.
p
25j 8
28.
31.
32.
33.
34.
35.
36.
Radical Functions
√
√
√
√
25a2
9w10
25x2 − 50x + 25
49x2 − 42x + 9
√
39.
25x2 + 90x + 81
p
25f 14
p
(3x + 6)12
40.
p
(9x − 8)12
37.
38.
41.
42.
43.
44.
45.
46.
√
36x2 + 36x + 9
√
4e2
p
4p10
√
25x12
p
25q 6
√
49. Given that
√ x < 0, place the radical expression 27x12 in simple radical
form. Check your solution on your calculator for x = −2.
16m2
p
(7x + 5)12
√
for x = −2.
16h12
47. Given√that x < 0, place the radical
expression 32x6 in simple radical form.
Check your solution on your calculator
for x = −2.
48. Given√that x < 0, place the radical
expression 54x8 in simple radical form.
Check your solution on your calculator
Version: Fall 2007
50. Given that
√ x < 0, place the radical expression 44x10 in simple radical
form. Check your solution on your calculator for x = −2.
In Exercises 51-54, follow the lead of
Example 17 in the narrative to simplify
the given radical expression and check
your result with your graphing calculator.
51. Given that
√ x < 4, place the radical expression x2 − 8x + 16 in simple
radical form. Use a graphing calculator
to show that the graphs of the original
expression and your simple radical form
agree for all values of x such that x < 4.
52. Given that√x ≥ −2, place the radical expression x2 + 4x + 4 in simple
radical form. Use a graphing calculator
to show that the graphs of the original
expression and your simple radical form
agree for all values of x such that x ≥ −2.
53. Given that
√ x ≥ 5, place the radical expression x2 − 10x + 25 in simple
radical form. Use a graphing calculator
to show that the graphs of the original
expression and your simple radical form
agree for all values of x such that x ≥ 5.
54. Given that√x < −1, place the radical expression x2 + 2x + 1 in simple
radical form. Use a graphing calculator
to show that the graphs of the original
expression and your simple radical form
agree for all values of x such that x < −1.
Section 9.2
Multiplication Properties of Radicals
In Exercises 55-72, place each radical
expression in simple radical form. Assume that all variables represent positive
numbers.
√
55.
9d13
√
56.
4k 2
√
57.
25x2 + 40x + 16
√
58.
9x2 − 30x + 25
p
59.
4j 11
60.
61.
62.
63.
64.
65.
66.
p
√
√
√
√
√
√
√
67.
903
In Exercises 73-80, place each given radical expression in simple radical form. Assume that all variables represent positive
numbers.
p
p
73.
2f 5 8f 3
74.
75.
76.
77.
16j 6
78.
25m2
79.
9e9
80.
√
√
3s3 243s3
√
√
2k 7 32k 3
√
√
2n9 8n3
√ √
2e9 8e3
√
√
5n9 125n3
√ √
3z 5 27z 3
√ √
3t7 27t3
4c5
25z 2
25h10
25b2
9s7
√
68.
69.
70.
71.
9e7
p
4p8
√
9d15
p
9q 10
√
72.
4w7
Version: Fall 2007
904
Chapter 9
Radical Functions
9.2 Answers
1.
3.
7.
√
3 2
√
4 7
9.
√
6 3
5.
11.
√
7 5
15.
√
7 2
17.
√
3 5
23.
√
2 6
√
12 14
√
45 7
25.
√
45 10
27.
(6x − 11)2
29.
5|f |
21.
4|m|
33.
(7x + 5)6
35.
|5x − 5|
37.
|5x + 9|
39.
(3x + 6)6
41.
|6x + 3|
43.
2p4 |p|
45.
5q 2 |q|
47.
√
−4x3 2
49.
√
3x6 3
√
5 2
13.
19.
31.
Version: Fall 2007
Section 9.2
Multiplication Properties of Radicals
51. −x + 4.
√ The graphs of y = −x +
4 and y = x2 − 8x + 16 follow. Note
that they agree for x < 4.
69.
2p4
71.
3q 5
73.
4f 4
75.
8k 5
77.
4e6
79.
9z 4
905
53. √
x − 5. The graphs of y = x − 5 and
y = x2 − 10x + 25 follow. Note that
they agree for x ≥ 5.
55.
√
3d6 d
57.
5x + 4
59.
√
2j 5 j
61.
5m
63.
√
2c2 c
65.
5h5
67.
√
3s3 s
Version: Fall 2007