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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 155 · 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.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  2. 2.What is 47²? =
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 31² and 32²?
  5. 5.How many whole numbers lie between 15² and 16²?
  6. 6.A square garden has an area of 1936 square m. How long is each side (in m)?
  7. 7.What is √5041? =
  8. 8.What is 22²? =
  9. 9.Which of these is a perfect square? (a) 139 (b) 121 (c) 137
  10. 10.What is 35²? =
  11. 11.What is 97²? =
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is 15²? =
  14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 625 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 27² and 28²?
  17. 17.Which of these is a perfect square? (a) 203 (b) 224 (c) 196
  18. 18.What is 49²? =
  19. 19.What is 48²? =
  20. 20.Which of these is a perfect square? (a) 1410 (b) 1409 (c) 1369
  21. 21.A square garden has an area of 900 square m. How long is each side (in m)?
  22. 22.How many whole numbers lie between 28² and 29²?
  23. 23.What is √3481? =
  24. 24.How many whole numbers lie between 32² and 33²?
  25. 25.What is 53²? =
  26. 26.A square garden has an area of 1681 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 39² and 40²?
  28. 28.What is √1764? =
  29. 29.Which of these is a perfect square? (a) 784 (b) 797 (c) 837
  30. 30.A square garden has an area of 25 square m. How long is each side (in m)?
  31. 31.What is √5776? =
  32. 32.What is the smallest whole number by which 108 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 52 must be divided to get a perfect square?
  34. 34.What is √3969? =
  35. 35.Which of these is a perfect square? (a) 900 (b) 919 (c) 915
  36. 36.What is √8836? =
  37. 37.How many whole numbers lie between 5² and 6²?
  38. 38.What is 19²? =
  39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  40. 40.Which of these is a perfect square? (a) 1502 (b) 1444 (c) 1475

Answer key

  1. 2
  2. 2209
  3. 196
  4. 62
  5. 30
  6. 44
  7. 71
  8. 484
  9. 121
  10. 1225
  11. 9409
  12. 841
  13. 225
  14. 49
  15. 25
  16. 54
  17. 196
  18. 2401
  19. 2304
  20. 1369
  21. 30
  22. 56
  23. 59
  24. 64
  25. 2809
  26. 41
  27. 78
  28. 42
  29. 784
  30. 5
  31. 76
  32. 3
  33. 13
  34. 63
  35. 900
  36. 94
  37. 10
  38. 361
  39. 676
  40. 1444

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