Name _________________________________________________ Class _______________ Date _______________
Practice
3-2
Perfect Cubes, Cube Roots, and Equations of the form x3 = p
3-2
Perfect Cubes, Cube Roots, and Equations of the form
1.Use the fact that –512 is a perfect cube to evaluate
or a simplified fraction.
2.Find the cube root
3
3
- 512 . Write an integer
- 64 .
3.Solve the equation w3 = 1,000.
1 . Simplify your answer. Write an integer, proper
125
fraction, or mixed number.
4.Solve the equation d3 =
5.Solve the equation v3 = 12. Use a calculator. Round to the nearest tenth.
6.The volume of a cube is 8 in.3. How long is each side?
7.a)Writing Evaluate
3
- 216 . Write an integer or a simplified fraction.
b) Explain how you can check that your result is correct.
8. Error Analysis On a math test, George writes 9 as the solution to the equation
d3 = 27.
a) Find the correct solution. Write an integer or a simplified fraction.
b) What error did George likely make on the test?
❍❍ A. George cubed 27.
❍❍ B. George divided 27 by 3.
❍❍ C. George multiplied 27 by 3.
❍❍ D. George divided 27 by 30.
27 . Simplify your
1, 000
answer. Write an integer, proper fraction, or mixed number.
9.a)Reasoning Find the value of z in the equation z3 =
b) If the cube of a number is less than 1, does it follow that the number must
be less than 1? Include examples to explain your reasoning.
c) If the cube of a positive number is greater than 1, does it follow that
the number must be greater than 1? Include examples to explain your
reasoning.
10. Estimation Solve for c in the equation c3 = 55.
a) Estimate using the perfect cube closest to 55.
b) Use a calculator to solve for c. Round to the nearest tenth.
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Practice 3-2
1
Homework G
11. Building Blocks A company is making building blocks. Each building block is a
cube and has volume 8 ft3. How long is each side of the building block?
343
12. a) Find the value of c for the equation c3 = 1,728.
b) The equation c2 = p can have zero, one, or two solutions. What can you say
about the number of solutions of the equation c3 = p? Explain.
13. Solve the equation v3 = 18 26 for v. Simplify your answer. Write an integer,
27
proper fraction, or a mixed number.
14. Challenge A family is packing their belongings to prepare for a trip. They use
a box that has the shape of a cube.
a) If the box has a volume of 86 ft3, what is the length of one side? Round to
the nearest tenth as needed.
b) The kids want to bring poster board to draw on. If the poster board is
square and has an area of 9 ft2, will the poster board fit in the box flat
against a side?
15. Challenge The Travers are adding a new room to their house. The room will
be a cube with volume 6,859 ft3. They are going to put in hardwood floors,
and the contractor charges $10 per square foot. How much will the
hardwood floors cost?
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Practice 3-2
2
Homework G
ANSWER
KEY
Practice 3-2: P
erfect Cubes, Cube Roots, and Equations of the
form x3 = p
1.–8
2.–4
3.w = 10
4.d = 1
5
5.v = 2.3
6.2 in.
7.a)–6
b)
Answers will vary
8.a)3
b)
B
9.a) 3
10
b)
Answers will vary
c)
Answers will vary
10. a) 4
b)
3.8
11. 2 ft
7
12. a) 12
b)
Answers will vary
13. v = 2 2
3
14. a) 4.4 ft
b)
Yes
15. $3,610
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Practice 3-2
3
Answer Key G