This document discusses cubes and cube roots. It defines a perfect cube as a number that is the cube of an integer. Perfect cubes have integer cube roots. The document provides examples of determining if a number is a perfect cube and finding the cube root of perfect cubes. It also discusses the relationships between side lengths, volumes, and cube root operations for cubes.

1. Cubes and Cube
Roots

2. Objective: You will be able to determine if a
number is a perfect cube and to find the cube root
of a number that is a perfect cube.

3. PERFECT CUBES
What does that mean?

4. 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 that number’s
square root.

5. 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.

6. Perfect Cubes and Cube Roots
Is 8 a perfect cube?
that number’s square root.

7. Perfect Cubes and Cube Roots
that.

8. Perfect Cubes and Cube Roots
that.

9. Perfect Cubes and Cube Roots
8 is a perfect cube and its cube root is 2

10. Perfect Cubes and Cube Roots
Is 5 a perfect cube?

11. Perfect Cubes and Cube Roots
Is 5 a perfect cube?

12. Perfect Cubes and Cube Roots
Three Dimensions
Perfect Cube
Volume

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

14. Cubes and Cubic Roots
3
27 = 3 or 3 = 27
3
Notice that 27 objects can be arranged into a cube
of 3 levels (high) of 3 rows and 3 columns.

15. Cube Root

3 cubed is 27, so the cube root of 27 is 3
3
27

The cube root of a number is ...
... a special value that when cubed gives the original
number.

The cube root of 27 is ...
... 3, because when 3 is cubed you get 27.

16. Perfect Cubes and Cube Roots
Side
Volume
Volume
Length Operation
Perfect
Cube
2 units 2 x 2 x 2
8
8 units3

17. Perfect Cubes and Cube Roots
Perfect Cube:
Cube Root
Volume: units3
Side Length: units

18. Perfect Cubes and Cube Roots
Volume
Side
Volume
Length Operation
Perfect
Cube
1 unit
1x1x1
1 units3
1
2 units 2 x 2 x 2
8 units3
8

19. Perfect Cubes and Cube Roots
Volume
Side
Volume
Length Operation
Perfect
Cube
1 unit
13
1 units3
1
2 units 23
8 units3
8
3 units 33
27 units3
27

20. Perfect Cubes and Cube Roots
Volume
Side
Volume
Length Operation
Perfect
Cube
1 unit
13
1 units3
1
2 units 23
8 units3
8
3 units 33
27 units3
27
4 units

21. Perfect Cubes and Cube Roots
Volume
Side
Volume
Length Operation
Perfect
Cube
1 unit
13
1 units3
1
2 units 23
8 units3
8
3 units 33
27 units3
27
4 units 43

22. Perfect Cubes and Cube Roots
Volume
Side
Volume
Length Operation
Perfect
Cube
1 unit
13
1 units3
1
2 units 23
8 units3
8
3 units 33
27 units3
27
4 units 43
64 units3

23. Perfect Cubes and Cube Roots
Volume
Side
Volume
Length Operation
Perfect
Cube
1 unit
13
1 units3
1
2 units 23
8 units3
8
3 units 33
27 units3
27
4 units 43
64 units3
64

24. Perfect Cubes and Cube Roots
Side
Volume
Length Operatio
n
Volume
Perfect
Cube
1 unit
13
1 units3
1
2 units 23
8 units3
8
3 units 33
27 units3
27
4 units 43
64 units3
64
S units S3
S3 units3
S3

25. Perfect Cubes and Cube Roots
Side
Volume
Volume
Length Operation of cube
of
cube
Perfect
Cube
1 unit
13
1 units3
1
2 units
23
8 units3
8
3 units
33
27 units3 27
4 units
43
64 units3 64
S units S3
10 units
S3 units3
S3

26. Perfect Cubes and Cube Roots
Side
Volume
Volume
Length Operation of cube
of
cube
Perfect
Cube
1 unit
13
1 units3
1
2 units
23
8 units3
8
3 units
33
27 units3 27
4 units
43
64 units3 64
S units S3
10 units 103
S3 units3
S3

27. Perfect Cubes and Cube Roots

28. Perfect Cubes and Cube Roots

29. Perfect Cubes and Cube Roots

30. Perfect Cubes and Cube Roots

31. Perfect Cubes and Cube Roots

32. Perfect Cubes and Cube Roots
Practice
Is 827 a perfect cube?

33. You Can Also Cube
Negative Numbers
 Have a look at this:
 If you cube 5 you get 125: 5 × 5 × 5 = 125
 If you cube -5 you get -125: -5 × -5 × -5 = -125
 So the cube root of -125 is -5

34. Perfect Cubes
 The Perfect Cubes are the cubes of the
whole numbers:
Perfect
Cubes
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15 etc
1
8
27
64
125
216
343
512
729
1000
1331
1728
2197
2744
3375
 It is easy to work out the cube root of a perfect
cube, but it is really hard to work out other cube
roots.
…

35. Conclusion: You can now determine if a number
is a perfect cube and find the cube root of a
number that is a perfect cube.