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# Cubes

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What is a perfect cube?
How do you find cube roots?

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### Cubes

1. 1. Cubes and Cube Roots
2. 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. 3. PERFECT CUBES What does that mean?
4. 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. 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. 6. Perfect Cubes and Cube Roots Is 8 a perfect cube? that number’s square root.
7. 7. Perfect Cubes and Cube Roots that.
8. 8. Perfect Cubes and Cube Roots that.
9. 9. Perfect Cubes and Cube Roots 8 is a perfect cube and its cube root is 2
10. 10. Perfect Cubes and Cube Roots Is 5 a perfect cube?
11. 11. Perfect Cubes and Cube Roots Is 5 a perfect cube?
12. 12. Perfect Cubes and Cube Roots Three Dimensions Perfect Cube Volume
13. 13. Perfect Cubes and Cube Roots Perfect Cube: 8 Cube Root 2 Volume: 8 units3 Side Length: 2 units
14. 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. 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. 16. Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube 2 units 2 x 2 x 2 8 8 units3
17. 17. Perfect Cubes and Cube Roots Perfect Cube: Cube Root Volume: units3 Side Length: units
18. 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. 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. 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. 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. 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. 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. 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. 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. 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. 27. Perfect Cubes and Cube Roots
28. 28. Perfect Cubes and Cube Roots
29. 29. Perfect Cubes and Cube Roots
30. 30. Perfect Cubes and Cube Roots
31. 31. Perfect Cubes and Cube Roots
32. 32. Perfect Cubes and Cube Roots Practice Is 827 a perfect cube?
33. 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. 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. 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.