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What is a perfect cube? How do you find cube roots?
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Cubes and Cube Cubes and Cube RootsRoots
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.
PERFECT CUBES PERFECT CUBES
What does that mean?What does that mean?
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.
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.
Perfect Cubes and Cube Roots
Is 8 a perfect cube?that number’s square root.
Perfect Cubes and Cube Roots
that.
Perfect Cubes and Cube Roots
that.
Perfect Cubes and Cube Roots
8 is a perfect cube and its cube root is 2
Perfect Cubes and Cube Roots
Is 5 a perfect cube?
Perfect Cubes and Cube Roots
Is 5 a perfect cube?
Perfect Cubes and Cube Roots
Three Dimensions
Perfect Cube
Volume
Perfect Cubes and Cube Roots
Perfect Cube: 8 Cube Root 2
Volume: 8 units3 Side Length: 2 units
Perfect Cubes and Cube Roots
Cubes and Cubic RootsCubes and Cubic Roots
33 27 3 3 27or
Notice that 27 objects can be arranged into a cube of 3 levels (high) of 3 rows and 3 columns.
Cube RootCube Root 3 cubed is 27, so the 3 cubed is 27, so the cube root of 27 is 3cube root of 27 is 3
33 2727
The cube root of a number is ...The cube root of a number is ...... a special value that when ... a special value that when cubedcubed gives the original gives the original number.number.
The cube root of The cube root of 2727 is ... is ...... ... 33, because , because when 3 is cubedwhen 3 is cubed you get you get 2727..
Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
2 units 2 x 2 x 2 8 units3 8
Perfect Cube: Cube Root
Volume: units3 Side Length: units
Perfect Cubes and Cube Roots
Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 1 x 1 x 1 1 units3 1
2 units 2 x 2 x 2 8 units3 8
Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units 23 8 units3 8
3 units 33 27 units3 27
Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units 23 8 units3 8
3 units 33 27 units3 27
4 units
Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units 23 8 units3 8
3 units 33 27 units3 27
4 units 43
Perfect Cubes and Cube Roots
Side Length
Volume Operation
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
Perfect Cubes and Cube Roots
Side Length
Volume Operation
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
Perfect Cubes and Cube Roots
Side Length
Volume Operation
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
Perfect Cubes and Cube Roots
Side Length of cube
Volume Operation
Volume 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 S3 units3 S3
10 units
Perfect Cubes and Cube Roots
Side Length of cube
Volume Operation
Volume 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 S3 units3 S3
10 units 103
Perfect Cubes and Cube Roots
Perfect Cubes and Cube Roots
Perfect Cubes and Cube Roots
Perfect Cubes and Cube Roots
Perfect Cubes and Cube Roots
Practice
Is 827 a perfect cube?
Perfect Cubes and Cube Roots
You Can Also Cube Negative You Can Also Cube Negative NumbersNumbers
Have a look at this: Have a look at this: If you cube 5 you get 125: 5 × 5 × 5 = 125If you cube 5 you get 125: 5 × 5 × 5 = 125 If you cube -5 you get -125: -5 × -5 × -5 = -125If you cube -5 you get -125: -5 × -5 × -5 = -125 So the So the cube rootcube root of -125 is -5 of -125 is -5
Perfect CubesPerfect Cubes The Perfect Cubes are the cubes of the The Perfect Cubes are the cubes of the
whole numbers::
It is easy to work out the cube root of a perfect It is easy to work out the cube root of a perfect cube, but it is cube, but it is really hardreally hard to work out other cube to work out other cube roots.roots.
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 …
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.
