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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 244 · 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 18² and 19²?
  2. 2.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 10² and 11²?
  4. 4.What is the smallest whole number by which 125 must be divided to get a perfect square?
  5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the smallest whole number by which 375 must be divided to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 819 (b) 784 (c) 833
  8. 8.Which of these is a perfect square? (a) 1225 (b) 1244 (c) 1284
  9. 9.What is √5329? =
  10. 10.What is the smallest whole number by which 486 must be divided to get a perfect square?
  11. 11.How many whole numbers lie between 34² and 35²?
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 24 must be divided to get a perfect square?
  14. 14.What is √900? =
  15. 15.What is √784? =
  16. 16.A square garden has an area of 3364 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 38² and 39²?
  18. 18.A square garden has an area of 64 square m. How long is each side (in m)?
  19. 19.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  20. 20.Which of these is a perfect square? (a) 1444 (b) 1496 (c) 1446
  21. 21.What is the smallest whole number by which 128 must be divided to get a perfect square?
  22. 22.How many whole numbers lie between 27² and 28²?
  23. 23.What is 47²? =
  24. 24.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 625 (b) 658 (c) 648
  26. 26.What is √8100? =
  27. 27.A square garden has an area of 100 square m. How long is each side (in m)?
  28. 28.Which of these is a perfect square? (a) 614 (b) 576 (c) 585
  29. 29.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 2916 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 637 must be divided to get a perfect square?
  32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 45² and 46²?
  34. 34.Which of these is a perfect square? (a) 1089 (b) 1115 (c) 1098
  35. 35.Which of these is a perfect square? (a) 1566 (b) 1552 (c) 1521
  36. 36.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  37. 37.What is 27²? =
  38. 38.What is √1444? =
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  40. 40.A square garden has an area of 2401 square m. How long is each side (in m)?

Answer key

  1. 36
  2. 676
  3. 20
  4. 5
  5. 144
  6. 15
  7. 784
  8. 1225
  9. 73
  10. 6
  11. 68
  12. 784
  13. 6
  14. 30
  15. 28
  16. 58
  17. 76
  18. 8
  19. 729
  20. 1444
  21. 2
  22. 54
  23. 2209
  24. 13
  25. 625
  26. 90
  27. 10
  28. 576
  29. 36
  30. 54
  31. 13
  32. 121
  33. 90
  34. 1089
  35. 1521
  36. 10
  37. 729
  38. 38
  39. 441
  40. 49

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