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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 440 · 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.Which of these is a perfect square? (a) 140 (b) 121 (c) 135
  2. 2.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is 67²? =
  4. 4.A square garden has an area of 1089 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  6. 6.A square garden has an area of 676 square m. How long is each side (in m)?
  7. 7.What is √484? =
  8. 8.Which of these is a perfect square? (a) 223 (b) 196 (c) 204
  9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 396 must be divided to get a perfect square?
  11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 27² and 28²?
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is √7569? =
  15. 15.What is √5776? =
  16. 16.How many whole numbers lie between 36² and 37²?
  17. 17.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  18. 18.What is 77²? =
  19. 19.How many whole numbers lie between 12² and 13²?
  20. 20.A square garden has an area of 64 square m. How long is each side (in m)?
  21. 21.What is √5929? =
  22. 22.Which of these is a perfect square? (a) 324 (b) 332 (c) 359
  23. 23.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √529? =
  25. 25.A square garden has an area of 81 square m. How long is each side (in m)?
  26. 26.What is √2704? =
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √5329? =
  29. 29.What is √9025? =
  30. 30.What is 42²? =
  31. 31.What is 71²? =
  32. 32.What is √841? =
  33. 33.What is √1089? =
  34. 34.What is √4761? =
  35. 35.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √784? =
  39. 39.How many whole numbers lie between 34² and 35²?
  40. 40.What is √2209? =

Answer key

  1. 121
  2. 484
  3. 4489
  4. 33
  5. 5
  6. 26
  7. 22
  8. 196
  9. 576
  10. 11
  11. 100
  12. 54
  13. 25
  14. 87
  15. 76
  16. 72
  17. 6
  18. 5929
  19. 24
  20. 8
  21. 77
  22. 324
  23. 676
  24. 23
  25. 9
  26. 52
  27. 121
  28. 73
  29. 95
  30. 1764
  31. 5041
  32. 29
  33. 33
  34. 69
  35. 15
  36. 169
  37. 64
  38. 28
  39. 68
  40. 47

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