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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 670 · 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 the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  2. 2.How many whole numbers lie between 11² and 12²?
  3. 3.What is √3844? =
  4. 4.What is 21²? =
  5. 5.A square garden has an area of 1296 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 46² and 47²?
  8. 8.What is √4900? =
  9. 9.How many whole numbers lie between 5² and 6²?
  10. 10.Which of these is a perfect square? (a) 784 (b) 799 (c) 804
  11. 11.A square garden has an area of 1444 square m. How long is each side (in m)?
  12. 12.What is 60²? =
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 1569 (b) 1539 (c) 1521
  15. 15.Which of these is a perfect square? (a) 100 (b) 107 (c) 120
  16. 16.What is 79²? =
  17. 17.What is 69²? =
  18. 18.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  19. 19.What is √3600? =
  20. 20.What is √9801? =
  21. 21.Which of these is a perfect square? (a) 1025 (b) 1024 (c) 1086
  22. 22.Which of these is a perfect square? (a) 169 (b) 174 (c) 193
  23. 23.Which of these is a perfect square? (a) 730 (b) 745 (c) 729
  24. 24.A square garden has an area of 3600 square m. How long is each side (in m)?
  25. 25.What is 12²? =
  26. 26.What is √1089? =
  27. 27.How many whole numbers lie between 6² and 7²?
  28. 28.What is 15²? =
  29. 29.A square garden has an area of 1089 square m. How long is each side (in m)?
  30. 30.What is √8649? =
  31. 31.How many whole numbers lie between 32² and 33²?
  32. 32.A square garden has an area of 1600 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is √5625? =
  35. 35.How many whole numbers lie between 15² and 16²?
  36. 36.A square garden has an area of 3249 square m. How long is each side (in m)?
  37. 37.Which of these is a perfect square? (a) 150 (b) 152 (c) 144
  38. 38.What is 49²? =
  39. 39.What is 23²? =
  40. 40.A square garden has an area of 1156 square m. How long is each side (in m)?

Answer key

  1. 121
  2. 22
  3. 62
  4. 441
  5. 36
  6. 64
  7. 92
  8. 70
  9. 10
  10. 784
  11. 38
  12. 3600
  13. 400
  14. 1521
  15. 100
  16. 6241
  17. 4761
  18. 13
  19. 60
  20. 99
  21. 1024
  22. 169
  23. 729
  24. 60
  25. 144
  26. 33
  27. 12
  28. 225
  29. 33
  30. 93
  31. 64
  32. 40
  33. 49
  34. 75
  35. 30
  36. 57
  37. 144
  38. 2401
  39. 529
  40. 34

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