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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 418 · 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 45²? =
  2. 2.Which of these is a perfect square? (a) 1296 (b) 1354 (c) 1323
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 100 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 137 (b) 121 (c) 132
  6. 6.What is √784? =
  7. 7.Which of these is a perfect square? (a) 556 (b) 529 (c) 558
  8. 8.What is 15²? =
  9. 9.Which of these is a perfect square? (a) 242 (b) 246 (c) 225
  10. 10.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  11. 11.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  13. 13.What is 98²? =
  14. 14.A square garden has an area of 1521 square m. How long is each side (in m)?
  15. 15.What is √8281? =
  16. 16.How many whole numbers lie between 31² and 32²?
  17. 17.A square garden has an area of 121 square m. How long is each side (in m)?
  18. 18.What is the smallest whole number by which 44 must be divided to get a perfect square?
  19. 19.What is √1849? =
  20. 20.What is 32²? =
  21. 21.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  22. 22.What is 49²? =
  23. 23.Which of these is a perfect square? (a) 1018 (b) 1011 (c) 961
  24. 24.How many whole numbers lie between 35² and 36²?
  25. 25.How many whole numbers lie between 17² and 18²?
  26. 26.How many whole numbers lie between 45² and 46²?
  27. 27.What is √6241? =
  28. 28.A square garden has an area of 25 square m. How long is each side (in m)?
  29. 29.What is 66²? =
  30. 30.How many whole numbers lie between 24² and 25²?
  31. 31.How many whole numbers lie between 11² and 12²?
  32. 32.How many whole numbers lie between 41² and 42²?
  33. 33.A square garden has an area of 1764 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  35. 35.What is 64²? =
  36. 36.What is √8464? =
  37. 37.What is 77²? =
  38. 38.What is √900? =
  39. 39.Which of these is a perfect square? (a) 576 (b) 584 (c) 613
  40. 40.What is √1369? =

Answer key

  1. 2025
  2. 1296
  3. 36
  4. 10
  5. 121
  6. 28
  7. 529
  8. 225
  9. 225
  10. 3
  11. 225
  12. 2
  13. 9604
  14. 39
  15. 91
  16. 62
  17. 11
  18. 11
  19. 43
  20. 1024
  21. 14
  22. 2401
  23. 961
  24. 70
  25. 34
  26. 90
  27. 79
  28. 5
  29. 4356
  30. 48
  31. 22
  32. 82
  33. 42
  34. 5
  35. 4096
  36. 92
  37. 5929
  38. 30
  39. 576
  40. 37

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