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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 645 · 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) 930 (b) 900 (c) 912
  2. 2.What is √1521? =
  3. 3.How many whole numbers lie between 41² and 42²?
  4. 4.A square garden has an area of 225 square m. How long is each side (in m)?
  5. 5.What is √8464? =
  6. 6.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  7. 7.What is the smallest whole number by which 216 must be divided to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 1600 (b) 1640 (c) 1667
  9. 9.Which of these is a perfect square? (a) 122 (b) 121 (c) 132
  10. 10.How many whole numbers lie between 7² and 8²?
  11. 11.How many whole numbers lie between 16² and 17²?
  12. 12.What is 85²? =
  13. 13.What is √1225? =
  14. 14.Which of these is a perfect square? (a) 1366 (b) 1296 (c) 1297
  15. 15.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 384 must be divided to get a perfect square?
  18. 18.How many whole numbers lie between 8² and 9²?
  19. 19.What is 62²? =
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 163 (b) 150 (c) 144
  22. 22.What is 16²? =
  23. 23.How many whole numbers lie between 39² and 40²?
  24. 24.How many whole numbers lie between 43² and 44²?
  25. 25.A square garden has an area of 49 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √2809? =
  28. 28.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  29. 29.Which of these is a perfect square? (a) 1109 (b) 1101 (c) 1089
  30. 30.Which of these is a perfect square? (a) 185 (b) 169 (c) 177
  31. 31.What is √625? =
  32. 32.What is √8100? =
  33. 33.A square garden has an area of 1024 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 45² and 46²?
  35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 294 must be divided to get a perfect square?
  37. 37.What is 67²? =
  38. 38.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  39. 39.What is 17²? =
  40. 40.A square garden has an area of 324 square m. How long is each side (in m)?

Answer key

  1. 900
  2. 39
  3. 82
  4. 15
  5. 92
  6. 7
  7. 6
  8. 1600
  9. 121
  10. 14
  11. 32
  12. 7225
  13. 35
  14. 1296
  15. 121
  16. 225
  17. 6
  18. 16
  19. 3844
  20. 784
  21. 144
  22. 256
  23. 78
  24. 86
  25. 7
  26. 49
  27. 53
  28. 361
  29. 1089
  30. 169
  31. 25
  32. 90
  33. 32
  34. 90
  35. 529
  36. 6
  37. 4489
  38. 13
  39. 289
  40. 18

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