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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 507 · 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 sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √5329? =
  3. 3.How many whole numbers lie between 50² and 51²?
  4. 4.How many whole numbers lie between 8² and 9²?
  5. 5.How many whole numbers lie between 10² and 11²?
  6. 6.What is √1089? =
  7. 7.Which of these is a perfect square? (a) 361 (b) 383 (c) 396
  8. 8.What is √9025? =
  9. 9.What is 42²? =
  10. 10.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 35²? =
  12. 12.How many whole numbers lie between 13² and 14²?
  13. 13.What is √144? =
  14. 14.A square garden has an area of 1681 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 861 (b) 847 (c) 841
  16. 16.What is √1296? =
  17. 17.Which of these is a perfect square? (a) 1426 (b) 1369 (c) 1372
  18. 18.What is 15²? =
  19. 19.What is √2209? =
  20. 20.A square garden has an area of 2500 square m. How long is each side (in m)?
  21. 21.A square garden has an area of 1369 square m. How long is each side (in m)?
  22. 22.What is 93²? =
  23. 23.What is 19²? =
  24. 24.How many whole numbers lie between 5² and 6²?
  25. 25.Which of these is a perfect square? (a) 182 (b) 176 (c) 169
  26. 26.A square garden has an area of 121 square m. How long is each side (in m)?
  27. 27.What is 47²? =
  28. 28.A square garden has an area of 1156 square m. How long is each side (in m)?
  29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 2304 square m. How long is each side (in m)?
  31. 31.A square garden has an area of 2401 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 35² and 36²?
  33. 33.A square garden has an area of 484 square m. How long is each side (in m)?
  34. 34.What is √361? =
  35. 35.A square garden has an area of 2704 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 46² and 47²?
  37. 37.What is √1156? =
  38. 38.A square garden has an area of 1444 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 20² and 21²?
  40. 40.A square garden has an area of 1936 square m. How long is each side (in m)?

Answer key

  1. 36
  2. 73
  3. 100
  4. 16
  5. 20
  6. 33
  7. 361
  8. 95
  9. 1764
  10. 100
  11. 1225
  12. 26
  13. 12
  14. 41
  15. 841
  16. 36
  17. 1369
  18. 225
  19. 47
  20. 50
  21. 37
  22. 8649
  23. 361
  24. 10
  25. 169
  26. 11
  27. 2209
  28. 34
  29. 625
  30. 48
  31. 49
  32. 70
  33. 22
  34. 19
  35. 52
  36. 92
  37. 34
  38. 38
  39. 40
  40. 44

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