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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 637 · 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 √196? =
  2. 2.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  3. 3.What is the smallest whole number by which 98 must be divided to get a perfect square?
  4. 4.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 40² and 41²?
  6. 6.What is 24²? =
  7. 7.What is 28²? =
  8. 8.What is 86²? =
  9. 9.How many whole numbers lie between 45² and 46²?
  10. 10.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  11. 11.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  12. 12.What is √4096? =
  13. 13.What is √625? =
  14. 14.What is √5329? =
  15. 15.What is √529? =
  16. 16.How many whole numbers lie between 49² and 50²?
  17. 17.Which of these is a perfect square? (a) 900 (b) 930 (c) 922
  18. 18.How many whole numbers lie between 42² and 43²?
  19. 19.What is the smallest whole number by which 150 must be divided to get a perfect square?
  20. 20.What is √2601? =
  21. 21.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 96²? =
  23. 23.What is 36²? =
  24. 24.Which of these is a perfect square? (a) 509 (b) 484 (c) 501
  25. 25.Which of these is a perfect square? (a) 144 (b) 159 (c) 155
  26. 26.A square garden has an area of 841 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 1225 square m. How long is each side (in m)?
  28. 28.What is 32²? =
  29. 29.What is √4900? =
  30. 30.What is 82²? =
  31. 31.How many whole numbers lie between 5² and 6²?
  32. 32.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  33. 33.How many whole numbers lie between 33² and 34²?
  34. 34.What is √8100? =
  35. 35.Which of these is a perfect square? (a) 225 (b) 226 (c) 247
  36. 36.What is the smallest whole number by which 50 must be divided to get a perfect square?
  37. 37.Which of these is a perfect square? (a) 1225 (b) 1244 (c) 1275
  38. 38.What is 59²? =
  39. 39.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  40. 40.Which of these is a perfect square? (a) 204 (b) 206 (c) 196

Answer key

  1. 14
  2. 10
  3. 2
  4. 2
  5. 80
  6. 576
  7. 784
  8. 7396
  9. 90
  10. 14
  11. 15
  12. 64
  13. 25
  14. 73
  15. 23
  16. 98
  17. 900
  18. 84
  19. 6
  20. 51
  21. 225
  22. 9216
  23. 1296
  24. 484
  25. 144
  26. 29
  27. 35
  28. 1024
  29. 70
  30. 6724
  31. 10
  32. 6
  33. 66
  34. 90
  35. 225
  36. 2
  37. 1225
  38. 3481
  39. 900
  40. 196

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