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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 459 · 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.How many whole numbers lie between 37² and 38²?
  2. 2.What is √729? =
  3. 3.What is √9025? =
  4. 4.What is 83²? =
  5. 5.How many whole numbers lie between 29² and 30²?
  6. 6.What is 56²? =
  7. 7.What is √1849? =
  8. 8.What is 20²? =
  9. 9.What is the smallest whole number by which 8 must be divided to get a perfect square?
  10. 10.What is 65²? =
  11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 1936 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 121 (b) 143 (c) 128
  14. 14.What is √1369? =
  15. 15.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  16. 16.A square garden has an area of 2704 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 28 must be divided to get a perfect square?
  18. 18.What is √625? =
  19. 19.What is √8464? =
  20. 20.What is 50²? =
  21. 21.What is 17²? =
  22. 22.Which of these is a perfect square? (a) 676 (b) 717 (c) 679
  23. 23.How many whole numbers lie between 9² and 10²?
  24. 24.A square garden has an area of 3364 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 1296 square m. How long is each side (in m)?
  26. 26.What is 34²? =
  27. 27.What is √2500? =
  28. 28.A square garden has an area of 841 square m. How long is each side (in m)?
  29. 29.What is 82²? =
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √3600? =
  33. 33.What is the smallest whole number by which 252 must be divided to get a perfect square?
  34. 34.A square garden has an area of 144 square m. How long is each side (in m)?
  35. 35.What is √3844? =
  36. 36.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  37. 37.What is √324? =
  38. 38.A square garden has an area of 3249 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  40. 40.What is 37²? =

Answer key

  1. 74
  2. 27
  3. 95
  4. 6889
  5. 58
  6. 3136
  7. 43
  8. 400
  9. 2
  10. 4225
  11. 625
  12. 44
  13. 121
  14. 37
  15. 7
  16. 52
  17. 7
  18. 25
  19. 92
  20. 2500
  21. 289
  22. 676
  23. 18
  24. 58
  25. 36
  26. 1156
  27. 50
  28. 29
  29. 6724
  30. 225
  31. 64
  32. 60
  33. 7
  34. 12
  35. 62
  36. 3
  37. 18
  38. 57
  39. 2
  40. 1369

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