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CC-11
Cube Roots
A cube number is a power with an exponent of 3. The cube of a whole
number is a perfect cube. 3 ∙ 3 ∙ 3 5 33 5 27.
8.EE.2 Use … cube root
symbols to represent
solutions to equations of the
form … x3 5 p, where p is
a positive rational number.
Evaluate … cube roots of
small perfect cubes …
Test Prep Tip
Volume is measured
in cubic units. Area is
measured in square units.
Length is measured in
linear units.
You can work backward from a perfect cube, such
as 27, to find the number 3. This is called a cube root.
The cube root of a number is another number that,
when raised to the third power, is equal to the given
number. The number 3 is the cube root of 27.
3
3
3
3
The symbol "
means the cube root of a number.
3
3 3
"
27 5 "
3 5 3.
Finding Cube Roots
A cube-shaped packing box has a volume of 64 cubic feet. What is
the side length of the box?
The formula for the volume V of a cube is V 5 s3 , where s is the
length of one side.
3
So, the length of one side s is "
V , the cube root of the volume V.
3
3
s5"
V5"
64 5 4
The side length of the box is 4 feet.
Think: 64 5 4 ∙ 4 ∙ 4
64 ft3
1. Find each cube root.
a.
3
"
125
b.
3
"
1
c.
3
"
512
You can find cube roots by solving equations of the form x3 = p.
To find the cube root of a fraction, find the cube root of the numerator
and the cube root of the denominator.
Use after Lesson 11-1.
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CC-11 Cube Roots
3 1
Å27
3
5
"1
3
"27
5 13
Solving Cube Root Equations
Test Prep Tip
One way to find a cube
root is to guess a number
and raise it to the third
power. The cube of an
even number will always
be even and the cube of
an odd number will always
be odd.
1
Solve x3 5 8 .
x3 5 18
d Write the equation.
3 3
"
x 5 3Å18
d Take the cube root of each side.
3
"1
5
d Rewrite the cube root of the fraction.
3
"8
x 5 12
d Simplify. Think: 1 5 1 ∙ 1 ∙ 1 and 8 5 2 ∙ 2 ∙ 2.
2. Solve each equation.
8
1
b. x3 5 27
a. x 3 5 2 1 6
c. x3 5 343
Homework Exercises
Find the side length of a cube with each given volume.
For
Exercises
See
Examples
1–9
1
10–15
2
1. 1,000 m3
2. 1 cm3
3. 729 ft3
Find each cube root.
3
3
4. "216
3
5. "8
3
6. "64
3
7. "27
3
343
9. "
8. "512
Solve each equation.
10. x3 5 125
1
11. x3 5 729
27
12. x3 5 216
512
13. x3 5 125
343
14. x3 5 729
15. x3 5 1,000
16. Guided Problem Solving Find the cube root of 0.008.
• Can you rename the decimal as a fraction?
• Write your answer as a decimal. Check by cubing your answer.
17. Find the cube root of 0.216.
18.
Writing in Math
Is 0.3 the cube root of 0.27? Explain.
19 a. Copy and complete the table below.
x
1
2
3
4
5
6
7
8
9
10
x2
x3
b. Are any of the numbers both a perfect square and a perfect cube?
c. When x is a perfect square, what is true about the cube of x?
CC-11 Cube Roots
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