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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 302 · 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 the smallest whole number by which 392 must be divided to get a perfect cube?
  2. 2.A big cube of edge 6 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  3. 3.Which of these is a perfect cube? (a) 729 (b) 771 (c) 789
  4. 4.What is the smallest whole number by which 128 must be multiplied to get a perfect cube?
  5. 5.What is the smallest whole number by which 5 must be multiplied to get a perfect cube?
  6. 6.What is ∛27? =
  7. 7.A cube has a volume of 2744 cubic cm. How long is each edge (in cm)?
  8. 8.A big cube of edge 6 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  9. 9.A cube has a volume of 125 cubic cm. How long is each edge (in cm)?
  10. 10.What is ∛5832? =
  11. 11.What is ∛343? =
  12. 12.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  13. 13.A big cube of edge 9 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  14. 14.Which of these is a perfect cube? (a) 1931 (b) 1982 (c) 1728
  15. 15.What is 13³? =
  16. 16.What is the smallest whole number by which 4 must be multiplied to get a perfect cube?
  17. 17.Which of these is a perfect cube? (a) 1237 (b) 1062 (c) 1000
  18. 18.What is the smallest whole number by which 7 must be multiplied to get a perfect cube?
  19. 19.What is the smallest whole number by which 500 must be multiplied to get a perfect cube?
  20. 20.What is 20³? =
  21. 21.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?
  22. 22.What is ∛1000? =
  23. 23.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  24. 24.A big cube of edge 15 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  25. 25.What is 19³? =
  26. 26.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  27. 27.A cube has a volume of 512 cubic cm. How long is each edge (in cm)?
  28. 28.A big cube of edge 16 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  29. 29.What is ∛2744? =
  30. 30.What is ∛3375? =
  31. 31.What is 11³? =
  32. 32.What is 12³? =
  33. 33.What is ∛6859? =
  34. 34.Which of these is a perfect cube? (a) 105 (b) 76 (c) 64
  35. 35.What is 15³? =
  36. 36.What is ∛4096? =
  37. 37.What is ∛13824? =
  38. 38.What is the smallest whole number by which 675 must be multiplied to get a perfect cube?
  39. 39.A big cube of edge 18 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  40. 40.What is the smallest whole number by which 72 must be divided to get a perfect cube?

Answer key

  1. 49
  2. 27
  3. 729
  4. 4
  5. 25
  6. 3
  7. 14
  8. 8
  9. 5
  10. 18
  11. 7
  12. 125
  13. 27
  14. 1728
  15. 2197
  16. 2
  17. 1000
  18. 49
  19. 2
  20. 8000
  21. 7
  22. 10
  23. 4
  24. 125
  25. 6859
  26. 27
  27. 8
  28. 64
  29. 14
  30. 15
  31. 1331
  32. 1728
  33. 19
  34. 64
  35. 3375
  36. 16
  37. 24
  38. 5
  39. 216
  40. 9

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