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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 224 · 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 784 square m. How long is each side (in m)?
  2. 2.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  3. 3.What is √169? =
  4. 4.A square garden has an area of 1764 square m. How long is each side (in m)?
  5. 5.How many whole numbers lie between 42² and 43²?
  6. 6.Which of these is a perfect square? (a) 110 (b) 118 (c) 100
  7. 7.What is √289? =
  8. 8.What is √4624? =
  9. 9.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  10. 10.What is √3249? =
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 1296 (b) 1346 (c) 1327
  13. 13.How many whole numbers lie between 11² and 12²?
  14. 14.Which of these is a perfect square? (a) 797 (b) 784 (c) 800
  15. 15.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  16. 16.Which of these is a perfect square? (a) 205 (b) 210 (c) 196
  17. 17.How many whole numbers lie between 6² and 7²?
  18. 18.A square garden has an area of 289 square m. How long is each side (in m)?
  19. 19.What is 25²? =
  20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 1546 (b) 1521 (c) 1524
  22. 22.How many whole numbers lie between 34² and 35²?
  23. 23.How many whole numbers lie between 49² and 50²?
  24. 24.What is 90²? =
  25. 25.What is √1849? =
  26. 26.What is the smallest whole number by which 832 must be divided to get a perfect square?
  27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 53²? =
  29. 29.How many whole numbers lie between 47² and 48²?
  30. 30.What is 95²? =
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √4225? =
  33. 33.A square garden has an area of 2809 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 1097 (b) 1149 (c) 1089
  35. 35.What is the smallest whole number by which 294 must be divided to get a perfect square?
  36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the smallest whole number by which 567 must be divided to get a perfect square?
  39. 39.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 121 (b) 126 (c) 128

Answer key

  1. 28
  2. 7
  3. 13
  4. 42
  5. 84
  6. 100
  7. 17
  8. 68
  9. 14
  10. 57
  11. 289
  12. 1296
  13. 22
  14. 784
  15. 14
  16. 196
  17. 12
  18. 17
  19. 625
  20. 225
  21. 1521
  22. 68
  23. 98
  24. 8100
  25. 43
  26. 13
  27. 529
  28. 2809
  29. 94
  30. 9025
  31. 64
  32. 65
  33. 53
  34. 1089
  35. 6
  36. 169
  37. 36
  38. 7
  39. 2
  40. 121

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