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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 657 · 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.A big cube of edge 4 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  2. 2.What is the smallest whole number by which 135 must be multiplied to get a perfect cube?
  3. 3.A cube has a volume of 2744 cubic cm. How long is each edge (in cm)?
  4. 4.What is ∛343? =
  5. 5.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  6. 6.What is the smallest whole number by which 3125 must be divided to get a perfect cube?
  7. 7.What is 12³? =
  8. 8.What is ∛10648? =
  9. 9.What is the smallest whole number by which 875 must be divided to get a perfect cube?
  10. 10.Which of these is a perfect cube? (a) 3211 (b) 3134 (c) 2744
  11. 11.What is the smallest whole number by which 7 must be divided to get a perfect cube?
  12. 12.What is 7³? =
  13. 13.What is 2³? =
  14. 14.A big cube of edge 18 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  15. 15.What is 6³? =
  16. 16.What is 13³? =
  17. 17.What is ∛6859? =
  18. 18.What is ∛5832? =
  19. 19.What is ∛13824? =
  20. 20.What is the smallest whole number by which 7 must be multiplied to get a perfect cube?
  21. 21.Which of these is a perfect cube? (a) 483 (b) 343 (c) 360
  22. 22.What is ∛216? =
  23. 23.Which of these is a perfect cube? (a) 34 (b) 44 (c) 27
  24. 24.What is ∛512? =
  25. 25.What is ∛1000? =
  26. 26.What is the smallest whole number by which 2 must be multiplied to get a perfect cube?
  27. 27.What is ∛3375? =
  28. 28.A cube has a volume of 4913 cubic cm. How long is each edge (in cm)?
  29. 29.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  30. 30.What is 20³? =
  31. 31.What is 3³? =
  32. 32.What is the smallest whole number by which 54 must be divided to get a perfect cube?
  33. 33.What is 8³? =
  34. 34.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  35. 35.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  36. 36.What is the smallest whole number by which 81 must be divided to get a perfect cube?
  37. 37.What is ∛8? =
  38. 38.What is ∛64? =
  39. 39.What is the smallest whole number by which 1323 must be multiplied to get a perfect cube?
  40. 40.What is the smallest whole number by which 448 must be divided to get a perfect cube?

Answer key

  1. 8
  2. 25
  3. 14
  4. 7
  5. 8
  6. 25
  7. 1728
  8. 22
  9. 7
  10. 2744
  11. 7
  12. 343
  13. 8
  14. 216
  15. 216
  16. 2197
  17. 19
  18. 18
  19. 24
  20. 49
  21. 343
  22. 6
  23. 27
  24. 8
  25. 10
  26. 4
  27. 15
  28. 17
  29. 12
  30. 8000
  31. 27
  32. 2
  33. 512
  34. 4
  35. 125
  36. 3
  37. 2
  38. 4
  39. 7
  40. 7

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