Name: Date: Lesson 1.6 Real-World Problems: Squares and Cubes: GROUP WORK
Find the two square roots of each number. Round your answer to the nearest tenth if necessary.
1. 81
2. 36
3. 97
4. 140
Find the cube root of each number. Round your answer to the nearest tenth if necessary.
5. 216
6. 343
7.
27
512
682
Solve each equation involving a variable that is squared.
9. h2 5 50.41
11. a2 5 144
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10. d 2 49
81
12. m2 5 295
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Solve each equation involving a variable that is cubed. Write fractions in simplest form, and round decimal answers to the nearest tenth.
14. s3
13. s 3 5 50.653
15. s 3 5 2,744
27
343
16. s 3 5 3,800
Solve. Show your work. Round to the nearest tenth.
17. The surface area of a spherical lampshade is 57.76π square inches. What is the radius of the lampshade?
18. A spherical solid of volume 123,456 cubic meters is melted and
the length of the cube?
recast into a solid cube. What is
19. A square box can store 2,940 cylindrical cans. Each cylindrical can occupies a
square base area of 15 square centimeters. What is the length of the box?
Area 15 cm2
?
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Lesson 1.6
1.
81 92 and − 81 − 92
5 9
5 29
2.
36 62 and 36 62
5 6
5 26
3.
≈ 9.8
 9.8 and 97 
97 4.
140 
≈ 11.8 and 140  11.8
5.
3
216 3 63
5 6
343 3 73
57
8.8
7. 3 682 
6.
8.
3
3
27
512
9.
3
33
3
8
3
8
or 0.4
h2 5 50.41
h2 50.41 or 50.41
h 7.1 or 7.1
10.
d2 49
81
72
72
or 2
2
9
9
7
7
d or 9
9
d2 11.
or 0.8 and
-0.8
a2 5 144
a 2 144 or 144
a 122 or 122
a 12 or 12
12.
m2 5 295
m2 295 or 295
m
 17.2 or 17.2
13.
s3 5 50.653
s 3 3 50.653
s 3.7
3
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14.
3
s3 27
343
s3 3
s
15.
33
73
3
7
or 0.4
s3 5 2,744
3
16.
s 3 3 2, 744
s 14
s3 5 3,800
3
s 3 3 3, 800
 15.6
s
17. Let the radius of the lampshade be r inches.
4pr2 5 57.76p
1
1
4π r 2 57.76π
4
4
π r 2 14.44π
14.44π
πr 2
π
π
r 2 14.44
r 2 14.44
r 3.82
r 3.8 in.
The length of the radius of the lampshade
is 3.8 inches.
18. Let the length of each side of the cube be
x meters.
x 3 123, 456
3
x 3 3 123, 456
 49.8 m
x The length of each side of the cube is
49.8 meters.
19. Area of square box 5 2,940 ? 15
5 44,100 cm2
Let the length of each side of the square box
be x centimeters.
x2 5 44,100
x 2 44,100
x 210 cm
The length of each side of the square box is
210 centimeters.
140 Answers
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