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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 844 · 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 625 must be multiplied to get a perfect cube?
  2. 2.What is the smallest whole number by which 5 must be divided to get a perfect cube?
  3. 3.Which of these is a perfect cube? (a) 1331 (b) 1516 (c) 1550
  4. 4.What is 16³? =
  5. 5.A big cube of edge 12 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  6. 6.What is the smallest whole number by which 200 must be multiplied to get a perfect cube?
  7. 7.A cube has a volume of 729 cubic cm. How long is each edge (in cm)?
  8. 8.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  9. 9.A big cube of edge 18 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  10. 10.A big cube of edge 15 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  11. 11.Which of these is a perfect cube? (a) 2509 (b) 2197 (c) 2666
  12. 12.What is ∛729? =
  13. 13.What is ∛2197? =
  14. 14.Which of these is a perfect cube? (a) 65 (b) 102 (c) 64
  15. 15.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  16. 16.What is ∛125? =
  17. 17.What is the smallest whole number by which 9 must be multiplied to get a perfect cube?
  18. 18.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  19. 19.What is ∛5832? =
  20. 20.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  21. 21.What is ∛3375? =
  22. 22.A big cube of edge 8 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  23. 23.What is the smallest whole number by which 189 must be divided to get a perfect cube?
  24. 24.What is the smallest whole number by which 243 must be multiplied to get a perfect cube?
  25. 25.What is ∛4913? =
  26. 26.What is the smallest whole number by which 500 must be divided to get a perfect cube?
  27. 27.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?
  28. 28.What is 18³? =
  29. 29.What is the smallest whole number by which 135 must be multiplied to get a perfect cube?
  30. 30.Which of these is a perfect cube? (a) 30 (b) 36 (c) 27
  31. 31.Which of these is a perfect cube? (a) 1728 (b) 1940 (c) 1992
  32. 32.Which of these is a perfect cube? (a) 1229 (b) 1022 (c) 1000
  33. 33.Which of these is a perfect cube? (a) 125 (b) 175 (c) 193
  34. 34.What is 20³? =
  35. 35.What is 9³? =
  36. 36.What is 3³? =
  37. 37.What is the smallest whole number by which 56 must be divided to get a perfect cube?
  38. 38.What is the smallest whole number by which 576 must be multiplied to get a perfect cube?
  39. 39.What is 19³? =
  40. 40.A big cube of edge 16 cm is cut into small cubes of edge 4 cm. How many small cubes are there?

Answer key

  1. 25
  2. 5
  3. 1331
  4. 4096
  5. 64
  6. 5
  7. 9
  8. 8
  9. 216
  10. 125
  11. 2197
  12. 9
  13. 13
  14. 64
  15. 16
  16. 5
  17. 3
  18. 12
  19. 18
  20. 4
  21. 15
  22. 8
  23. 7
  24. 3
  25. 17
  26. 4
  27. 7
  28. 5832
  29. 25
  30. 27
  31. 1728
  32. 1000
  33. 125
  34. 8000
  35. 729
  36. 27
  37. 7
  38. 3
  39. 6859
  40. 64

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