Name _________________________________________________________ Date _________
5.1
Practice A
In Exercises 1–3, find the indicated real nth root(s) of a.
1. n  3, a  125
2. n  2, a  49
3. n  4, a  81
In Exercises 4–9, evaluate the expression without using a calculator.
14
4. 271 3
5. 16
7. 6253 4
8.
6. 43 2
10002 3
9. 321 5
In Exercises 10–15, evaluate the expression using a calculator. Round your
answer to two decimal places when appropriate.
10.
5
16,807
11.
6
12. 121 3
15,625
54
13. 921 5
15. 113 3 4
14. 6561
In Exercises 16 and 17, find the radius of the figure with the given volume.
16. V  1726 in.3
17. V  734 m3
In Exercises 18–23, find the real solution(s) of the equation. Round your answer
to two decimal places when appropriate.
18. x 4  256
21.
 x  73
 1000
 x  62
 40
19. 3x3  375
20.
22. x5  112
23. 9 x 4  54
24. When the average price of an item increases from p1 to p2 over a period of
n years, the price p 2 is given by p2  p1 r  1 , where r is the annual rate
n
of inflation (in decimal form). Find the annual rate of inflation when the price
of a loaf of bread was $1.19 in 1970 and $3.29 in 2010.
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Name_________________________________________________________
5.1
Date __________
Practice B
In Exercises 1–3, find the indicated real nth root(s) of a.
1. n  3, a  343
2. n  6, a   64
3. n  5, a   243
In Exercises 4–9, evaluate the expression without using a calculator.
4. 363 2
7.
5. 163 4
1255 3
8. 256 5
6.
4
322 5
9. 27
4 3
In Exercises 10–15, evaluate the expression using a calculator. Round your
answer to two decimal places when appropriate.
10. 281 5
13. 750 2
12. 40,3516 7
11. 1502 5
5
14.

5
223

3
15.

7
 34

5
In Exercises 16 and 17, find the radius of the figure with the given volume.
16. V  425 in.3
17. V  1458 m3
In Exercises 18–23, find the real solution(s) of the equation. Round your answer
to two decimal places when appropriate.
18. 6 x 4  60
19. x5   233
20. x 4  19  100
21. x3  17  57
22. 1 x 4  125
5
23. 1 x3   49
7
24. Kepler’s third law states that the relationship between the mean distance d
(in astronomical units) of a planet from the Sun and the time t (in years) it
takes the planet to orbit the Sun can be given by d 3  t 2 .
a. It takes Venus 0.616 year to orbit the Sun. Find the mean distance of
Venus from the Sun (in astronomical units).
b. The mean distance of Jupiter from the Sun is 5.24 astronomical units.
How many years does it take Jupiter to orbit the Sun?
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