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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 357 · 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.A square garden has an area of 2500 square m. How long is each side (in m)?
  2. 2.What is √8100? =
  3. 3.What is √6084? =
  4. 4.Which of these is a perfect square? (a) 707 (b) 688 (c) 676
  5. 5.A square garden has an area of 400 square m. How long is each side (in m)?
  6. 6.What is 73²? =
  7. 7.A square garden has an area of 529 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 593 (b) 576 (c) 620
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 272 (b) 282 (c) 256
  11. 11.How many whole numbers lie between 38² and 39²?
  12. 12.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 1369 square m. How long is each side (in m)?
  14. 14.What is 29²? =
  15. 15.How many whole numbers lie between 39² and 40²?
  16. 16.What is 28²? =
  17. 17.What is 15²? =
  18. 18.What is √441? =
  19. 19.What is √625? =
  20. 20.A square garden has an area of 324 square m. How long is each side (in m)?
  21. 21.What is √4096? =
  22. 22.A square garden has an area of 841 square m. How long is each side (in m)?
  23. 23.What is √1024? =
  24. 24.How many whole numbers lie between 36² and 37²?
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  26. 26.Which of these is a perfect square? (a) 761 (b) 731 (c) 729
  27. 27.A square garden has an area of 1089 square m. How long is each side (in m)?
  28. 28.What is 48²? =
  29. 29.What is 21²? =
  30. 30.How many whole numbers lie between 14² and 15²?
  31. 31.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  32. 32.What is 71²? =
  33. 33.What is √1225? =
  34. 34.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  35. 35.What is the smallest whole number by which 44 must be divided to get a perfect square?
  36. 36.A square garden has an area of 3600 square m. How long is each side (in m)?
  37. 37.What is √1521? =
  38. 38.Which of these is a perfect square? (a) 331 (b) 324 (c) 329
  39. 39.What is 84²? =
  40. 40.What is 11²? =

Answer key

  1. 50
  2. 90
  3. 78
  4. 676
  5. 20
  6. 5329
  7. 23
  8. 576
  9. 256
  10. 256
  11. 76
  12. 900
  13. 37
  14. 841
  15. 78
  16. 784
  17. 225
  18. 21
  19. 25
  20. 18
  21. 64
  22. 29
  23. 32
  24. 72
  25. 36
  26. 729
  27. 33
  28. 2304
  29. 441
  30. 28
  31. 11
  32. 5041
  33. 35
  34. 14
  35. 11
  36. 60
  37. 39
  38. 324
  39. 7056
  40. 121

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