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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 117 · 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) 592 (b) 581 (c) 576
  2. 2.Which of these is a perfect square? (a) 163 (b) 144 (c) 146
  3. 3.A square garden has an area of 196 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 45² and 46²?
  6. 6.How many whole numbers lie between 35² and 36²?
  7. 7.How many whole numbers lie between 16² and 17²?
  8. 8.Which of these is a perfect square? (a) 256 (b) 266 (c) 271
  9. 9.How many whole numbers lie between 10² and 11²?
  10. 10.What is √196? =
  11. 11.What is 13²? =
  12. 12.How many whole numbers lie between 42² and 43²?
  13. 13.A square garden has an area of 121 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  15. 15.A square garden has an area of 484 square m. How long is each side (in m)?
  16. 16.Which of these is a perfect square? (a) 247 (b) 235 (c) 225
  17. 17.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  18. 18.What is 49²? =
  19. 19.A square garden has an area of 256 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 39² and 40²?
  21. 21.What is 88²? =
  22. 22.What is √6724? =
  23. 23.Which of these is a perfect square? (a) 347 (b) 324 (c) 356
  24. 24.What is 56²? =
  25. 25.What is 37²? =
  26. 26.How many whole numbers lie between 13² and 14²?
  27. 27.What is 31²? =
  28. 28.A square garden has an area of 3025 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 7² and 8²?
  30. 30.What is 18²? =
  31. 31.Which of these is a perfect square? (a) 395 (b) 384 (c) 361
  32. 32.Which of these is a perfect square? (a) 128 (b) 137 (c) 121
  33. 33.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  34. 34.What is √8836? =
  35. 35.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  37. 37.What is √5776? =
  38. 38.What is 22²? =
  39. 39.How many whole numbers lie between 29² and 30²?
  40. 40.What is the smallest whole number by which 504 must be multiplied to get a perfect square?

Answer key

  1. 576
  2. 144
  3. 14
  4. 11
  5. 90
  6. 70
  7. 32
  8. 256
  9. 20
  10. 14
  11. 169
  12. 84
  13. 11
  14. 15
  15. 22
  16. 225
  17. 5
  18. 2401
  19. 16
  20. 78
  21. 7744
  22. 82
  23. 324
  24. 3136
  25. 1369
  26. 26
  27. 961
  28. 55
  29. 14
  30. 324
  31. 361
  32. 121
  33. 3
  34. 94
  35. 13
  36. 13
  37. 76
  38. 484
  39. 58
  40. 14

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