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Name Class Date Practice
Form K
Roots and Radical Expressions
Find all the real square roots of each number.
1. 625
2. -1.44
16
3. 81
Find all the real cube roots of each number.
4. -216
1
5. 64
6. 0.027
Find all the real fourth roots of each number.
7. 0.2401
9. -1296
8. 1
Find each real root. To start, fi nd a number whose square, cube, or fourth is
equal to the radicand.
10. 1400
= 2(20)2
4
11. - 1256
3
12. 1 -729
Simplify each radical expression. Use absolute value symbols when needed.
To start, write the factors of the radicand as perfect squares, cubes, or fourths.
13. 225x 6
= 2(5)2(x3)2
3
14. 2343x 9y 12
4
15. 216x 16y 20
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Name Class Date Practice (continued)
Form K
Roots and Radical Expressions
3
16. The formula for the volume of a sphere is V = 4
3 pr . Solving for r, the radius of
3 3V
3
a sphere is r = 5
4p . If the volume of a sphere is 20 ft , what is the radius of the
sphere to the nearest hundredth?
Find the two real solutions of each equation.
17. x4 = 81
2401
19. x4 = 625
18. x2 = 144
20. Writing Explain how you know whether or not to include the absolute value
symbol on your root.
3
3
6
21. Arrange the numbers 1 -64, - 1 -64, 164, and 164, in order from least to
greatest.
22. Open-Ended Write a radical that has no real values.
23. Reasoning There are no real nth roots of a number b. What can you conclude
about the index n and the number b?
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Name Class Date Practice
Form G
Roots and Radical Expressions
Find all the real square roots of each number.
2. -196
1. 400
3. 10,000
4. 0.0625
7. -0.064
1000
8. 27
Find all the real cube roots of each number.
6. -343
5. 216
Find all the real fourth roots of each number.
9. -81
10. 256
11. 0.0001
12. 625
14. - 125
15. 1-0.01
16. 10.001
Find each real root.
13. 1144
4
17. 10.0081
3
3
3
18. 127
19. 1 -27
20. 10.09
Simplify each radical expression. Use absolute value symbols when needed.
21. 281x 4
3
22. 2121y 10
5
3
23. 28g 6
3
24. 2125x 9
25. 2243x 5y 15
27. 225(x + 2)4
28. 5343
29. 1 -0.008
31. 236x 2y 6
32. 2(m - n)4
4
x4
30. 581
3
64x9
26. 2(x - 9)3
3
4
33. A cube has volume V = s3 , where s is the length of a side. Find the side length
for a cube with volume 8000 cm3.
34. The temperature T in degrees Celsius ( °C ) of a liquid t minutes after heating is
given by the formula T = 8 1t. When is the temperature 48°C?
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Name Class Date Practice (continued)
Form G
Roots and Radical Expressions
Find the two real solutions of each equation.
35. x2 = 4
36. x4 = 81
37. x2 = 0.16
16
38. x2 = 49
16
39. x4 = 625
40. x2 = 121
625
41. x2 = 0.000009
42. x4 = 0.0001
43. The number of new customers n that visit a dry cleaning shop in one year
is directly related to the amount a (in dollars) spent on advertising. This
relationship is represented by n3 = 13,824a. To attract 480 new customers,
how much should the owners spend on advertising during the year?
44. Geometry The volume V of a sphere with radius r is given by the formula
V = 43 pr 3 .
a. What is the radius of a sphere with volume 36p cubic inches?
b. If the volume increases by a factor of 8, what is the new radius?
45. A clothing manufacturer finds the number of defective blouses d is a function
of the total number of blouses n produced at her factory. This function is
d = 0.000005n2 .
a. What is the total number of blouses produced if 45 are defective?
b. If the number of defective blouses increases by a factor of 9, how does the
total number of blouses change?
46. The velocity of a falling object can be found using the formula v 2 = 64h,
where v is the velocity (in feet per second) and h is the distance the object has
already fallen.
a. What is the velocity of the object after a 10-foot fall?
b. How much does the velocity increase if the object falls 20 feet
rather than 10 feet?
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