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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 664 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.How many whole numbers lie between 17² and 18²?
  2. 2.Which of these is a perfect square? (a) 100 (b) 114 (c) 115
  3. 3.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 529 square m. How long is each side (in m)?
  5. 5.What is 38²? =
  6. 6.What is 12²? =
  7. 7.What is 73²? =
  8. 8.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 41²? =
  10. 10.How many whole numbers lie between 47² and 48²?
  11. 11.What is the smallest whole number by which 125 must be divided to get a perfect square?
  12. 12.What is √1089? =
  13. 13.Which of these is a perfect square? (a) 330 (b) 324 (c) 346
  14. 14.How many whole numbers lie between 42² and 43²?
  15. 15.What is √3481? =
  16. 16.How many whole numbers lie between 6² and 7²?
  17. 17.A square garden has an area of 2704 square m. How long is each side (in m)?
  18. 18.What is √4356? =
  19. 19.Which of these is a perfect square? (a) 811 (b) 789 (c) 784
  20. 20.What is √5776? =
  21. 21.What is 32²? =
  22. 22.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  23. 23.A square garden has an area of 3481 square m. How long is each side (in m)?
  24. 24.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  26. 26.How many whole numbers lie between 43² and 44²?
  27. 27.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  28. 28.A square garden has an area of 1764 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  30. 30.What is √3136? =
  31. 31.What is 84²? =
  32. 32.How many whole numbers lie between 10² and 11²?
  33. 33.How many whole numbers lie between 5² and 6²?
  34. 34.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 65²? =
  36. 36.Which of these is a perfect square? (a) 233 (b) 247 (c) 225
  37. 37.A square garden has an area of 81 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 56 must be divided to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 487 (b) 508 (c) 484
  40. 40.What is √1024? =

Answer key

  1. 34
  2. 100
  3. 144
  4. 23
  5. 1444
  6. 144
  7. 5329
  8. 121
  9. 1681
  10. 94
  11. 5
  12. 33
  13. 324
  14. 84
  15. 59
  16. 12
  17. 52
  18. 66
  19. 784
  20. 76
  21. 1024
  22. 196
  23. 59
  24. 484
  25. 49
  26. 86
  27. 7
  28. 42
  29. 5
  30. 56
  31. 7056
  32. 20
  33. 10
  34. 784
  35. 4225
  36. 225
  37. 9
  38. 14
  39. 484
  40. 32

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