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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 613 · 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 135 must be divided to get a perfect square?
  2. 2.A square garden has an area of 961 square m. How long is each side (in m)?
  3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  4. 4.Which of these is a perfect square? (a) 483 (b) 462 (c) 441
  5. 5.What is the smallest whole number by which 75 must be divided to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 106 (b) 110 (c) 100
  7. 7.How many whole numbers lie between 36² and 37²?
  8. 8.Which of these is a perfect square? (a) 289 (b) 301 (c) 293
  9. 9.What is 73²? =
  10. 10.What is √5184? =
  11. 11.What is √961? =
  12. 12.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 44² and 45²?
  14. 14.What is √2025? =
  15. 15.What is 81²? =
  16. 16.Which of these is a perfect square? (a) 729 (b) 782 (c) 748
  17. 17.What is 56²? =
  18. 18.How many whole numbers lie between 5² and 6²?
  19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √4761? =
  21. 21.Which of these is a perfect square? (a) 1302 (b) 1296 (c) 1354
  22. 22.What is √1156? =
  23. 23.Which of these is a perfect square? (a) 159 (b) 152 (c) 144
  24. 24.How many whole numbers lie between 35² and 36²?
  25. 25.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √5625? =
  27. 27.A square garden has an area of 256 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 324 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 21² and 22²?
  30. 30.What is the smallest whole number by which 45 must be divided to get a perfect square?
  31. 31.A square garden has an area of 361 square m. How long is each side (in m)?
  32. 32.What is 15²? =
  33. 33.What is √625? =
  34. 34.How many whole numbers lie between 18² and 19²?
  35. 35.A square garden has an area of 2916 square m. How long is each side (in m)?
  36. 36.What is √3721? =
  37. 37.Which of these is a perfect square? (a) 1148 (b) 1089 (c) 1149
  38. 38.What is 61²? =
  39. 39.What is 58²? =
  40. 40.A square garden has an area of 25 square m. How long is each side (in m)?

Answer key

  1. 15
  2. 31
  3. 529
  4. 441
  5. 3
  6. 100
  7. 72
  8. 289
  9. 5329
  10. 72
  11. 31
  12. 625
  13. 88
  14. 45
  15. 6561
  16. 729
  17. 3136
  18. 10
  19. 841
  20. 69
  21. 1296
  22. 34
  23. 144
  24. 70
  25. 121
  26. 75
  27. 16
  28. 18
  29. 42
  30. 5
  31. 19
  32. 225
  33. 25
  34. 36
  35. 54
  36. 61
  37. 1089
  38. 3721
  39. 3364
  40. 5

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