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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 722 · 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 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  2. 2.What is 5³? =
  3. 3.A big cube of edge 15 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  4. 4.What is ∛512? =
  5. 5.What is the smallest whole number by which 7 must be multiplied to get a perfect cube?
  6. 6.What is ∛343? =
  7. 7.What is the smallest whole number by which 1323 must be divided to get a perfect cube?
  8. 8.A big cube of edge 12 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  9. 9.What is the smallest whole number by which 1080 must be multiplied to get a perfect cube?
  10. 10.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?
  11. 11.What is ∛4096? =
  12. 12.Which of these is a perfect cube? (a) 955 (b) 729 (c) 967
  13. 13.What is the smallest whole number by which 576 must be multiplied to get a perfect cube?
  14. 14.What is the smallest whole number by which 243 must be multiplied to get a perfect cube?
  15. 15.What is the smallest whole number by which 9 must be divided to get a perfect cube?
  16. 16.What is the smallest whole number by which 3 must be divided to get a perfect cube?
  17. 17.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  18. 18.What is ∛1000? =
  19. 19.What is the smallest whole number by which 500 must be divided to get a perfect cube?
  20. 20.A big cube of edge 6 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  21. 21.What is ∛12167? =
  22. 22.A cube has a volume of 125 cubic cm. How long is each edge (in cm)?
  23. 23.A cube has a volume of 1331 cubic cm. How long is each edge (in cm)?
  24. 24.A cube has a volume of 8 cubic cm. How long is each edge (in cm)?
  25. 25.What is 2³? =
  26. 26.A cube has a volume of 27 cubic cm. How long is each edge (in cm)?
  27. 27.What is the smallest whole number by which 200 must be multiplied to get a perfect cube?
  28. 28.What is 13³? =
  29. 29.What is ∛6859? =
  30. 30.What is 14³? =
  31. 31.What is ∛729? =
  32. 32.Which of these is a perfect cube? (a) 3375 (b) 3559 (c) 3754
  33. 33.A big cube of edge 4 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  34. 34.What is the smallest whole number by which 56 must be divided to get a perfect cube?
  35. 35.What is ∛1728? =
  36. 36.What is 8³? =
  37. 37.What is ∛8000? =
  38. 38.A big cube of edge 8 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  39. 39.What is the smallest whole number by which 3136 must be multiplied to get a perfect cube?
  40. 40.What is the smallest whole number by which 6125 must be divided to get a perfect cube?

Answer key

  1. 27
  2. 125
  3. 125
  4. 8
  5. 49
  6. 7
  7. 49
  8. 216
  9. 25
  10. 7
  11. 16
  12. 729
  13. 3
  14. 3
  15. 9
  16. 3
  17. 19
  18. 10
  19. 4
  20. 27
  21. 23
  22. 5
  23. 11
  24. 2
  25. 8
  26. 3
  27. 5
  28. 2197
  29. 19
  30. 2744
  31. 9
  32. 3375
  33. 64
  34. 7
  35. 12
  36. 512
  37. 20
  38. 64
  39. 7
  40. 49

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