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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 694 · 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 55²? =
  2. 2.A square garden has an area of 2116 square m. How long is each side (in m)?
  3. 3.What is √3600? =
  4. 4.How many whole numbers lie between 27² and 28²?
  5. 5.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √5184? =
  7. 7.What is √5776? =
  8. 8.What is the smallest whole number by which 75 must be divided to get a perfect square?
  9. 9.Which of these is a perfect square? (a) 1253 (b) 1237 (c) 1225
  10. 10.A square garden has an area of 3364 square m. How long is each side (in m)?
  11. 11.What is 94²? =
  12. 12.What is √1089? =
  13. 13.How many whole numbers lie between 28² and 29²?
  14. 14.What is 98²? =
  15. 15.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  16. 16.What is 44²? =
  17. 17.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 176 must be divided to get a perfect square?
  19. 19.Which of these is a perfect square? (a) 655 (b) 625 (c) 641
  20. 20.What is √1849? =
  21. 21.Which of these is a perfect square? (a) 729 (b) 783 (c) 730
  22. 22.Which of these is a perfect square? (a) 1070 (b) 1024 (c) 1073
  23. 23.What is √2304? =
  24. 24.What is 56²? =
  25. 25.What is √361? =
  26. 26.What is the smallest whole number by which 98 must be divided to get a perfect square?
  27. 27.What is 46²? =
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 529 square m. How long is each side (in m)?
  31. 31.What is 70²? =
  32. 32.A square garden has an area of 1369 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 48² and 49²?
  34. 34.A square garden has an area of 2916 square m. How long is each side (in m)?
  35. 35.What is √6400? =
  36. 36.What is √7744? =
  37. 37.What is 33²? =
  38. 38.What is 22²? =
  39. 39.A square garden has an area of 144 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 39² and 40²?

Answer key

  1. 3025
  2. 46
  3. 60
  4. 54
  5. 64
  6. 72
  7. 76
  8. 3
  9. 1225
  10. 58
  11. 8836
  12. 33
  13. 56
  14. 9604
  15. 3
  16. 1936
  17. 625
  18. 11
  19. 625
  20. 43
  21. 729
  22. 1024
  23. 48
  24. 3136
  25. 19
  26. 2
  27. 2116
  28. 100
  29. 25
  30. 23
  31. 4900
  32. 37
  33. 96
  34. 54
  35. 80
  36. 88
  37. 1089
  38. 484
  39. 12
  40. 78

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