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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 189 · 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.Which of these is a perfect square? (a) 113 (b) 109 (c) 100
  2. 2.Which of these is a perfect square? (a) 121 (b) 135 (c) 136
  3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 81²? =
  5. 5.A square garden has an area of 2916 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 540 must be divided to get a perfect square?
  7. 7.What is 26²? =
  8. 8.How many whole numbers lie between 14² and 15²?
  9. 9.How many whole numbers lie between 32² and 33²?
  10. 10.A square garden has an area of 1369 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 37²? =
  13. 13.What is √7921? =
  14. 14.A square garden has an area of 121 square m. How long is each side (in m)?
  15. 15.What is 32²? =
  16. 16.How many whole numbers lie between 42² and 43²?
  17. 17.What is 14²? =
  18. 18.What is the smallest whole number by which 96 must be divided to get a perfect square?
  19. 19.What is 62²? =
  20. 20.How many whole numbers lie between 44² and 45²?
  21. 21.Which of these is a perfect square? (a) 448 (b) 441 (c) 481
  22. 22.What is 75²? =
  23. 23.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 49 square m. How long is each side (in m)?
  25. 25.Which of these is a perfect square? (a) 1156 (b) 1220 (c) 1158
  26. 26.Which of these is a perfect square? (a) 224 (b) 208 (c) 196
  27. 27.What is the smallest whole number by which 27 must be divided to get a perfect square?
  28. 28.Which of these is a perfect square? (a) 960 (b) 900 (c) 958
  29. 29.How many whole numbers lie between 33² and 34²?
  30. 30.A square garden has an area of 225 square m. How long is each side (in m)?
  31. 31.What is 34²? =
  32. 32.How many whole numbers lie between 35² and 36²?
  33. 33.What is 43²? =
  34. 34.What is √4624? =
  35. 35.What is √6241? =
  36. 36.What is 38²? =
  37. 37.How many whole numbers lie between 15² and 16²?
  38. 38.What is √900? =
  39. 39.What is √1296? =
  40. 40.A square garden has an area of 3136 square m. How long is each side (in m)?

Answer key

  1. 100
  2. 121
  3. 361
  4. 6561
  5. 54
  6. 15
  7. 676
  8. 28
  9. 64
  10. 37
  11. 676
  12. 1369
  13. 89
  14. 11
  15. 1024
  16. 84
  17. 196
  18. 6
  19. 3844
  20. 88
  21. 441
  22. 5625
  23. 6
  24. 7
  25. 1156
  26. 196
  27. 3
  28. 900
  29. 66
  30. 15
  31. 1156
  32. 70
  33. 1849
  34. 68
  35. 79
  36. 1444
  37. 30
  38. 30
  39. 36
  40. 56

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