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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 151 · 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 275 must be divided to get a perfect square?
  2. 2.What is 33²? =
  3. 3.How many whole numbers lie between 22² and 23²?
  4. 4.What is √3364? =
  5. 5.What is the smallest whole number by which 396 must be divided to get a perfect square?
  6. 6.What is 68²? =
  7. 7.How many whole numbers lie between 25² and 26²?
  8. 8.A square garden has an area of 1936 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 28² and 29²?
  10. 10.What is √2116? =
  11. 11.A square garden has an area of 1681 square m. How long is each side (in m)?
  12. 12.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  13. 13.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  14. 14.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  15. 15.What is 27²? =
  16. 16.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  17. 17.A square garden has an area of 324 square m. How long is each side (in m)?
  18. 18.What is the smallest whole number by which 18 must be divided to get a perfect square?
  19. 19.What is √361? =
  20. 20.How many whole numbers lie between 27² and 28²?
  21. 21.What is √900? =
  22. 22.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 28 must be divided to get a perfect square?
  24. 24.What is √5329? =
  25. 25.What is 81²? =
  26. 26.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  27. 27.What is the smallest whole number by which 20 must be divided to get a perfect square?
  28. 28.A square garden has an area of 2116 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 9² and 10²?
  30. 30.A square garden has an area of 1764 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 1332 (b) 1364 (c) 1296
  32. 32.Which of these is a perfect square? (a) 450 (b) 474 (c) 441
  33. 33.A square garden has an area of 2401 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 1434 (b) 1430 (c) 1369
  35. 35.How many whole numbers lie between 36² and 37²?
  36. 36.How many whole numbers lie between 16² and 17²?
  37. 37.What is 93²? =
  38. 38.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  39. 39.What is √121? =
  40. 40.What is √3136? =

Answer key

  1. 11
  2. 1089
  3. 44
  4. 58
  5. 11
  6. 4624
  7. 50
  8. 44
  9. 56
  10. 46
  11. 41
  12. 6
  13. 2
  14. 14
  15. 729
  16. 13
  17. 18
  18. 2
  19. 19
  20. 54
  21. 30
  22. 225
  23. 7
  24. 73
  25. 6561
  26. 3
  27. 5
  28. 46
  29. 18
  30. 42
  31. 1296
  32. 441
  33. 49
  34. 1369
  35. 72
  36. 32
  37. 8649
  38. 11
  39. 11
  40. 56

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