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 K
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. Simplify the expression
3
125 .
13. Find the value of w. Use a calculator. Round to the nearest tenth.
w3 = 3,087
14. Think About the Process
8 , what does the solution look like
1, 331
when you have taken the cube root of each side but have not yet done any
calculating?
a) When solving the equation w3 =
8
1, 331
8
❍❍ B.w = 3
1, 331
❍❍ C.w = 3 8
1, 331
8
❍❍ D.w3 = 3
1, 331
❍❍ A.w =
3
b) Solve for w.
15. Think About the Process The zoo is creating a new tank for some of its fish.
The zoo wants the tank to be a cube and be able to hold 3,375 ft3 of water.
a) Which of these equations would you solve to find the length of each side
of the tank?
❍❍ A.3V = 3,375
3, 375
❍❍ B.
= s3
3
❍❍ C.V3 = 3,375
❍❍ D.3,375 = s3
b) Each side of the tank is
ft long.
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Practice 3-2
2
Homework K
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. 5
13. w ≈ 14.6
14. a) B
b)
w≈ 2
11
15. a) D
b)
15
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Practice 3-2
3
Answer Key K