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.
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
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.