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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 287 · 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 15 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 181 (b) 169 (c) 192
  3. 3.A square garden has an area of 1681 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 441 (b) 471 (c) 449
  5. 5.What is the smallest whole number by which 135 must be divided to get a perfect square?
  6. 6.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √3025? =
  8. 8.A square garden has an area of 676 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  10. 10.Which of these is a perfect square? (a) 1369 (b) 1425 (c) 1403
  11. 11.A square garden has an area of 64 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 45² and 46²?
  13. 13.What is 45²? =
  14. 14.A square garden has an area of 625 square m. How long is each side (in m)?
  15. 15.What is √8100? =
  16. 16.Which of these is a perfect square? (a) 376 (b) 361 (c) 399
  17. 17.How many whole numbers lie between 27² and 28²?
  18. 18.What is √5929? =
  19. 19.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  20. 20.How many whole numbers lie between 12² and 13²?
  21. 21.What is √7225? =
  22. 22.A square garden has an area of 169 square m. How long is each side (in m)?
  23. 23.What is √3721? =
  24. 24.What is 66²? =
  25. 25.A square garden has an area of 1849 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 1516 (b) 1444 (c) 1473
  27. 27.What is √7396? =
  28. 28.What is √3600? =
  29. 29.What is √8464? =
  30. 30.Which of these is a perfect square? (a) 100 (b) 108 (c) 103
  31. 31.What is 57²? =
  32. 32.How many whole numbers lie between 33² and 34²?
  33. 33.Which of these is a perfect square? (a) 1678 (b) 1600 (c) 1662
  34. 34.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  35. 35.A square garden has an area of 1089 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 52²? =
  38. 38.How many whole numbers lie between 20² and 21²?
  39. 39.What is 42²? =
  40. 40.What is √3481? =

Answer key

  1. 225
  2. 169
  3. 41
  4. 441
  5. 15
  6. 625
  7. 55
  8. 26
  9. 11
  10. 1369
  11. 8
  12. 90
  13. 2025
  14. 25
  15. 90
  16. 361
  17. 54
  18. 77
  19. 3
  20. 24
  21. 85
  22. 13
  23. 61
  24. 4356
  25. 43
  26. 1444
  27. 86
  28. 60
  29. 92
  30. 100
  31. 3249
  32. 66
  33. 1600
  34. 5
  35. 33
  36. 289
  37. 2704
  38. 40
  39. 1764
  40. 59

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