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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 697 · 40 sums
TalentJR

The method (Threes make cubes): Cube: n × n × n. Cube root: the number that, used three times, gives the cube. Units digits: 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0 — use them to guess cube roots. Make a perfect cube: break into primes; multiply by what completes each group of three (or divide by what is left over). A big cube of edge a cut into small cubes of edge b gives (a ÷ b)³ small cubes.

NameDateTime takenScore ___ / 40
  1. 1.What is ∛216? =
  2. 2.What is the smallest whole number by which 54 must be divided to get a perfect cube?
  3. 3.What is the smallest whole number by which 128 must be multiplied to get a perfect cube?
  4. 4.Which of these is a perfect cube? (a) 2197 (b) 2207 (c) 2405
  5. 5.What is ∛2744? =
  6. 6.Which of these is a perfect cube? (a) 133 (b) 125 (c) 181
  7. 7.A big cube of edge 6 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  8. 8.What is ∛8000? =
  9. 9.A cube has a volume of 8000 cubic cm. How long is each edge (in cm)?
  10. 10.A cube has a volume of 5832 cubic cm. How long is each edge (in cm)?
  11. 11.A cube has a volume of 216 cubic cm. How long is each edge (in cm)?
  12. 12.What is 12³? =
  13. 13.What is ∛343? =
  14. 14.What is ∛12167? =
  15. 15.What is the smallest whole number by which 4 must be multiplied to get a perfect cube?
  16. 16.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  17. 17.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  18. 18.What is ∛1000? =
  19. 19.What is 2³? =
  20. 20.What is the smallest whole number by which 5400 must be multiplied to get a perfect cube?
  21. 21.What is the smallest whole number by which 49 must be divided to get a perfect cube?
  22. 22.A big cube of edge 4 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  23. 23.What is 19³? =
  24. 24.What is the smallest whole number by which 2 must be multiplied to get a perfect cube?
  25. 25.A cube has a volume of 3375 cubic cm. How long is each edge (in cm)?
  26. 26.Which of these is a perfect cube? (a) 1971 (b) 1807 (c) 1728
  27. 27.Which of these is a perfect cube? (a) 521 (b) 611 (c) 512
  28. 28.What is ∛1728? =
  29. 29.A cube has a volume of 125 cubic cm. How long is each edge (in cm)?
  30. 30.What is 7³? =
  31. 31.What is the smallest whole number by which 432 must be multiplied to get a perfect cube?
  32. 32.What is ∛9261? =
  33. 33.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  34. 34.What is 13³? =
  35. 35.What is ∛15625? =
  36. 36.What is ∛512? =
  37. 37.What is 14³? =
  38. 38.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?
  39. 39.What is 10³? =
  40. 40.What is the smallest whole number by which 320 must be multiplied to get a perfect cube?

Answer key

  1. 6
  2. 2
  3. 4
  4. 2197
  5. 14
  6. 125
  7. 27
  8. 20
  9. 20
  10. 18
  11. 6
  12. 1728
  13. 7
  14. 23
  15. 2
  16. 12
  17. 125
  18. 10
  19. 8
  20. 5
  21. 49
  22. 8
  23. 6859
  24. 4
  25. 15
  26. 1728
  27. 512
  28. 12
  29. 5
  30. 343
  31. 4
  32. 21
  33. 27
  34. 2197
  35. 25
  36. 8
  37. 2744
  38. 7
  39. 1000
  40. 25

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