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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 557 · 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 33²? =
  2. 2.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 196 (b) 197 (c) 219
  4. 4.What is 15²? =
  5. 5.How many whole numbers lie between 47² and 48²?
  6. 6.What is √4225? =
  7. 7.What is √1849? =
  8. 8.How many whole numbers lie between 11² and 12²?
  9. 9.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 18² and 19²?
  11. 11.What is √3721? =
  12. 12.Which of these is a perfect square? (a) 1563 (b) 1521 (c) 1559
  13. 13.What is the smallest whole number by which 125 must be divided to get a perfect square?
  14. 14.How many whole numbers lie between 46² and 47²?
  15. 15.Which of these is a perfect square? (a) 676 (b) 706 (c) 695
  16. 16.How many whole numbers lie between 43² and 44²?
  17. 17.Which of these is a perfect square? (a) 789 (b) 810 (c) 784
  18. 18.What is √3025? =
  19. 19.What is 65²? =
  20. 20.What is √5776? =
  21. 21.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  22. 22.How many whole numbers lie between 19² and 20²?
  23. 23.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  24. 24.What is √2401? =
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1681 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is 40²? =
  31. 31.How many whole numbers lie between 15² and 16²?
  32. 32.A square garden has an area of 100 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is √3249? =
  35. 35.What is √1764? =
  36. 36.How many whole numbers lie between 25² and 26²?
  37. 37.What is 66²? =
  38. 38.What is 51²? =
  39. 39.A square garden has an area of 1369 square m. How long is each side (in m)?
  40. 40.What is √5625? =

Answer key

  1. 1089
  2. 900
  3. 196
  4. 225
  5. 94
  6. 65
  7. 43
  8. 22
  9. 3
  10. 36
  11. 61
  12. 1521
  13. 5
  14. 92
  15. 676
  16. 86
  17. 784
  18. 55
  19. 4225
  20. 76
  21. 625
  22. 38
  23. 5
  24. 49
  25. 36
  26. 484
  27. 41
  28. 144
  29. 196
  30. 1600
  31. 30
  32. 10
  33. 529
  34. 57
  35. 42
  36. 50
  37. 4356
  38. 2601
  39. 37
  40. 75

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