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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 2 · 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 20 must be divided to get a perfect square?
  2. 2.What is 67²? =
  3. 3.What is √361? =
  4. 4.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  5. 5.What is √1936? =
  6. 6.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  7. 7.A square garden has an area of 3364 square m. How long is each side (in m)?
  8. 8.What is √1444? =
  9. 9.Which of these is a perfect square? (a) 1225 (b) 1227 (c) 1270
  10. 10.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 424 (b) 413 (c) 400
  12. 12.What is √625? =
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the smallest whole number by which 396 must be divided to get a perfect square?
  15. 15.What is 33²? =
  16. 16.Which of these is a perfect square? (a) 388 (b) 361 (c) 362
  17. 17.Which of these is a perfect square? (a) 959 (b) 951 (c) 900
  18. 18.What is 27²? =
  19. 19.How many whole numbers lie between 45² and 46²?
  20. 20.A square garden has an area of 1681 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 484 (b) 490 (c) 523
  22. 22.What is the smallest whole number by which 640 must be divided to get a perfect square?
  23. 23.What is √256? =
  24. 24.How many whole numbers lie between 28² and 29²?
  25. 25.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  26. 26.What is √5041? =
  27. 27.What is 61²? =
  28. 28.Which of these is a perfect square? (a) 352 (b) 346 (c) 324
  29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 81 square m. How long is each side (in m)?
  31. 31.How many whole numbers lie between 48² and 49²?
  32. 32.What is 22²? =
  33. 33.What is the smallest whole number by which 250 must be divided to get a perfect square?
  34. 34.What is 86²? =
  35. 35.How many whole numbers lie between 15² and 16²?
  36. 36.A square garden has an area of 1764 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 13² and 14²?
  38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 1849 square m. How long is each side (in m)?
  40. 40.What is √4356? =

Answer key

  1. 5
  2. 4489
  3. 19
  4. 3
  5. 44
  6. 11
  7. 58
  8. 38
  9. 1225
  10. 15
  11. 400
  12. 25
  13. 196
  14. 11
  15. 1089
  16. 361
  17. 900
  18. 729
  19. 90
  20. 41
  21. 484
  22. 10
  23. 16
  24. 56
  25. 3
  26. 71
  27. 3721
  28. 324
  29. 900
  30. 9
  31. 96
  32. 484
  33. 10
  34. 7396
  35. 30
  36. 42
  37. 26
  38. 361
  39. 43
  40. 66

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