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What is a perfect cube?

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

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Cubes Cubes Presentation Transcript

  • Cubes and Cube Roots
  • 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 What does that mean?
  • 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.
  • 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
  • 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.
  • 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.
  • Perfect Cubes and Cube Roots Side Volume Volume Length Operation Perfect Cube 2 units 2 x 2 x 2 8 8 units3
  • Perfect Cubes and Cube Roots Perfect Cube: Cube Root Volume: units3 Side Length: units
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Perfect Cubes and Cube Roots Practice Is 827 a perfect cube?
  • 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
  • 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. …
  • 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.