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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 116 · 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 √1681? =
  2. 2.A square garden has an area of 1369 square m. How long is each side (in m)?
  3. 3.What is the smallest whole number by which 125 must be divided to get a perfect square?
  4. 4.What is √7744? =
  5. 5.What is 64²? =
  6. 6.What is 29²? =
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 1349 (b) 1296 (c) 1309
  9. 9.How many whole numbers lie between 37² and 38²?
  10. 10.What is √484? =
  11. 11.What is √169? =
  12. 12.How many whole numbers lie between 12² and 13²?
  13. 13.Which of these is a perfect square? (a) 356 (b) 328 (c) 324
  14. 14.A square garden has an area of 144 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 1296 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 48² and 49²?
  17. 17.What is 86²? =
  18. 18.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  19. 19.How many whole numbers lie between 40² and 41²?
  20. 20.What is 84²? =
  21. 21.How many whole numbers lie between 44² and 45²?
  22. 22.A square garden has an area of 1024 square m. How long is each side (in m)?
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √7569? =
  25. 25.Which of these is a perfect square? (a) 289 (b) 318 (c) 303
  26. 26.What is √6724? =
  27. 27.What is √121? =
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 36 square m. How long is each side (in m)?
  30. 30.How many whole numbers lie between 11² and 12²?
  31. 31.A square garden has an area of 1936 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 36² and 37²?
  33. 33.What is √3025? =
  34. 34.What is √9409? =
  35. 35.What is the smallest whole number by which 405 must be divided to get a perfect square?
  36. 36.Which of these is a perfect square? (a) 916 (b) 900 (c) 956
  37. 37.What is √5476? =
  38. 38.Which of these is a perfect square? (a) 196 (b) 206 (c) 221
  39. 39.What is the smallest whole number by which 640 must be divided to get a perfect square?
  40. 40.What is 59²? =

Answer key

  1. 41
  2. 37
  3. 5
  4. 88
  5. 4096
  6. 841
  7. 729
  8. 1296
  9. 74
  10. 22
  11. 13
  12. 24
  13. 324
  14. 12
  15. 36
  16. 96
  17. 7396
  18. 784
  19. 80
  20. 7056
  21. 88
  22. 32
  23. 196
  24. 87
  25. 289
  26. 82
  27. 11
  28. 36
  29. 6
  30. 22
  31. 44
  32. 72
  33. 55
  34. 97
  35. 5
  36. 900
  37. 74
  38. 196
  39. 10
  40. 3481

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