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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 247 · 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 26²? =
  2. 2.What is √7396? =
  3. 3.Which of these is a perfect square? (a) 324 (b) 358 (c) 346
  4. 4.A square garden has an area of 361 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 281 (b) 256 (c) 273
  6. 6.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  7. 7.What is the smallest whole number by which 250 must be divided to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 144 (b) 146 (c) 154
  9. 9.How many whole numbers lie between 47² and 48²?
  10. 10.What is √5476? =
  11. 11.How many whole numbers lie between 8² and 9²?
  12. 12.A square garden has an area of 81 square m. How long is each side (in m)?
  13. 13.What is 83²? =
  14. 14.What is √5776? =
  15. 15.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 31²? =
  18. 18.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  19. 19.What is 25²? =
  20. 20.A square garden has an area of 1764 square m. How long is each side (in m)?
  21. 21.What is 23²? =
  22. 22.What is 70²? =
  23. 23.What is 16²? =
  24. 24.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  25. 25.What is √676? =
  26. 26.What is the smallest whole number by which 405 must be divided to get a perfect square?
  27. 27.What is 88²? =
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √3844? =
  30. 30.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  31. 31.What is √4489? =
  32. 32.How many whole numbers lie between 12² and 13²?
  33. 33.A square garden has an area of 25 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 441 (b) 455 (c) 459
  35. 35.What is 64²? =
  36. 36.What is 52²? =
  37. 37.What is 73²? =
  38. 38.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  39. 39.A square garden has an area of 2704 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 956 (b) 917 (c) 900

Answer key

  1. 676
  2. 86
  3. 324
  4. 19
  5. 256
  6. 7
  7. 10
  8. 144
  9. 94
  10. 74
  11. 16
  12. 9
  13. 6889
  14. 76
  15. 900
  16. 289
  17. 961
  18. 13
  19. 625
  20. 42
  21. 529
  22. 4900
  23. 256
  24. 13
  25. 26
  26. 5
  27. 7744
  28. 100
  29. 62
  30. 3
  31. 67
  32. 24
  33. 5
  34. 441
  35. 4096
  36. 2704
  37. 5329
  38. 3
  39. 52
  40. 900

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