1. CUBE ROOTS

2. Perfect Squares and Square Roots
Remember:
A number is a perfect square if you can take that many 1 x 1 unit squares and form them into a square. The side length of the square you form is that number’s square root.

4. Cube Root Vocabulary
radical sign
index
radicand

5. The index of a cube root is always 3.
Cube Roots
The index of a cube root is always 3.
The cube root of 64 is written as

6. Perfect Cubes and Cube Roots
Squares and Cubes:
Similarities
- All sides congruent
- All angles 90 degrees
Differences:
- Square is 2 dimensional
- Cube is 3 dimensional

7. Perfect Cubes and Cube Roots
Remember:
A cube is a three dimensional prism with 6 square faces; so all sides are congruent and all angles are right angles.

8. Perfect Cubes and Cube Roots
A number is a perfect cube if you can take that many 1 x 1 x 1 unit cubes and form them into a cube. The side length of the cube you form is that number’s cube root.

9. Perfect Cubes and Cube Roots
Perfect Cube: 1 Cube Root: 1
Volume: 1 units3 Side Length: 1 unit

10. Perfect Cubes and Cube Roots
Perfect Cube: 8 Cube Root: 2
Volume: 8 units3 Side Length: 2 units

11. Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume
Perfect Cube
1 unit
1 x 1 x 1
1 unit³ 1
2 units
2 x 2 x 2
8 units3 8
3 units
4 units
5 units

13. Find the cube roots:
𝟑 𝟏𝟐𝟓
𝟑 𝟏 𝟖
- 𝟑 −𝟐𝟕
𝟑 𝟏 𝟐𝟏𝟔
𝟑 − 𝟔𝟒 𝟏𝟎𝟎𝟎

14. A fish tank in the shape of a cube has a volume of 343 units³
A fish tank in the shape of a cube has a volume of 343 units³. What is the length of one side of the tank?
A cube has a volume of 125 units³. What is the length of one side?

15. Chloe wants to build a storage container in the shape of a cube to hold 216 cubic meters of hay for her horse. What is the length of one side of the container?

16. A Rubik’s Cube has a volume of 27 cubic centimeters. What is the surface area of one side of the cube?
An aquarium in the shape of a cube will hold 64 cubic feet of water. What would be the length of one side of the aquarium?