Name: ______________________
Class: __________________
AU8: Notes #3 – Cube Roots
Date: __________________
Warm-up:
Chloe wants to build a storage container in the shape of a cube to hold 125 cubic meters
of hay for her horse. Find the length of one side of the container.
Vocabulary:
When you use a number as a factor three times, you are cubing that number or raising it to the
third power. For example: 4 3  64 .
Numbers whose cube roots are integers or quotients of integers are called perfect cubes.
Let’s list some other perfect cubes that you know.
x
1
2
3
4
5
6
7
8
9
10
64
125
216
343
512
729
1,000
x3
Let’s look at the inverse of cubing:
n
3
1
8
27
n
Every number (positive, negative, or zero) have exactly one cube root.
Solve the following equations:
r3  8
x 3  125
1
Example A: Evaluate the following cube roots or solve the equations.
1.
3
729
2.
x 3  1000
3.
3
512
4.
x 3  216
5.
3
8
64
6.
3
0.125
Special Cases: Negative Cube Roots
Solve the following and explain:
r 3  8
x 3  125
Evaluate the following:
3
 729
3
2
 512
Real-World Problems:
The volume of a Rubik’s cube is 216 cm3, what is the length of one of its sides?
Find the radius of a spherical globe with a volume of 288π in3.
Try It!
a. Find the volume of a cube if the side length is 4 feet.
b. Dylan has a planter in the shape of a cube that holds 8 cubic feet of potting soil. Solve the
equation 8  s 3 to find the side length s of the container.
3