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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 716 · 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 √8649? =
  2. 2.What is 51²? =
  3. 3.What is √5184? =
  4. 4.What is √5929? =
  5. 5.What is √729? =
  6. 6.What is √196? =
  7. 7.What is √5476? =
  8. 8.What is √1089? =
  9. 9.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  10. 10.What is √2209? =
  11. 11.What is 58²? =
  12. 12.Which of these is a perfect square? (a) 582 (b) 576 (c) 599
  13. 13.How many whole numbers lie between 34² and 35²?
  14. 14.A square garden has an area of 225 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 484 (b) 494 (c) 521
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 48²? =
  18. 18.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  21. 21.What is the smallest whole number by which 32 must be divided to get a perfect square?
  22. 22.What is 24²? =
  23. 23.A square garden has an area of 1764 square m. How long is each side (in m)?
  24. 24.How many whole numbers lie between 50² and 51²?
  25. 25.What is √3249? =
  26. 26.What is 49²? =
  27. 27.What is the smallest whole number by which 405 must be divided to get a perfect square?
  28. 28.What is the smallest whole number by which 160 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 31² and 32²?
  30. 30.Which of these is a perfect square? (a) 196 (b) 205 (c) 218
  31. 31.What is the smallest whole number by which 135 must be divided to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 734 (b) 729 (c) 730
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  35. 35.How many whole numbers lie between 35² and 36²?
  36. 36.What is 87²? =
  37. 37.What is 35²? =
  38. 38.What is √6889? =
  39. 39.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  40. 40.What is √4096? =

Answer key

  1. 93
  2. 2601
  3. 72
  4. 77
  5. 27
  6. 14
  7. 74
  8. 33
  9. 7
  10. 47
  11. 3364
  12. 576
  13. 68
  14. 15
  15. 484
  16. 484
  17. 2304
  18. 100
  19. 256
  20. 2
  21. 2
  22. 576
  23. 42
  24. 100
  25. 57
  26. 2401
  27. 5
  28. 10
  29. 62
  30. 196
  31. 15
  32. 729
  33. 121
  34. 5
  35. 70
  36. 7569
  37. 1225
  38. 83
  39. 3
  40. 64

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