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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 567 · 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.How many whole numbers lie between 40² and 41²?
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 400 (b) 411 (c) 402
  4. 4.What is the smallest whole number by which 18 must be divided to get a perfect square?
  5. 5.A square garden has an area of 81 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is 36²? =
  8. 8.What is 37²? =
  9. 9.What is 51²? =
  10. 10.How many whole numbers lie between 15² and 16²?
  11. 11.What is √7396? =
  12. 12.What is √2809? =
  13. 13.A square garden has an area of 1521 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 104 (b) 112 (c) 100
  15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √2025? =
  17. 17.A square garden has an area of 1089 square m. How long is each side (in m)?
  18. 18.A square garden has an area of 1156 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 32 must be divided to get a perfect square?
  20. 20.What is 29²? =
  21. 21.What is √1521? =
  22. 22.How many whole numbers lie between 30² and 31²?
  23. 23.What is the smallest whole number by which 63 must be divided to get a perfect square?
  24. 24.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 26²? =
  26. 26.What is 82²? =
  27. 27.What is √5625? =
  28. 28.What is √576? =
  29. 29.What is 31²? =
  30. 30.A square garden has an area of 256 square m. How long is each side (in m)?
  31. 31.What is 60²? =
  32. 32.What is √1296? =
  33. 33.What is √2916? =
  34. 34.What is 21²? =
  35. 35.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  36. 36.What is 73²? =
  37. 37.A square garden has an area of 2401 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 1482 (b) 1444 (c) 1515
  39. 39.Which of these is a perfect square? (a) 713 (b) 676 (c) 708
  40. 40.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 80
  2. 64
  3. 400
  4. 2
  5. 9
  6. 256
  7. 1296
  8. 1369
  9. 2601
  10. 30
  11. 86
  12. 53
  13. 39
  14. 100
  15. 225
  16. 45
  17. 33
  18. 34
  19. 2
  20. 841
  21. 39
  22. 60
  23. 7
  24. 289
  25. 676
  26. 6724
  27. 75
  28. 24
  29. 961
  30. 16
  31. 3600
  32. 36
  33. 54
  34. 441
  35. 3
  36. 5329
  37. 49
  38. 1444
  39. 676
  40. 169

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