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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 513 · 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.Which of these is a perfect square? (a) 1305 (b) 1296 (c) 1358
  2. 2.Which of these is a perfect square? (a) 1389 (b) 1397 (c) 1369
  3. 3.What is 78²? =
  4. 4.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is 54²? =
  6. 6.Which of these is a perfect square? (a) 388 (b) 364 (c) 361
  7. 7.A square garden has an area of 1444 square m. How long is each side (in m)?
  8. 8.What is 60²? =
  9. 9.What is √5929? =
  10. 10.A square garden has an area of 2025 square m. How long is each side (in m)?
  11. 11.How many whole numbers lie between 44² and 45²?
  12. 12.Which of these is a perfect square? (a) 1444 (b) 1478 (c) 1455
  13. 13.What is 65²? =
  14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 35² and 36²?
  16. 16.What is √3844? =
  17. 17.What is √2209? =
  18. 18.How many whole numbers lie between 23² and 24²?
  19. 19.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  20. 20.How many whole numbers lie between 34² and 35²?
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  22. 22.Which of these is a perfect square? (a) 1562 (b) 1521 (c) 1592
  23. 23.How many whole numbers lie between 25² and 26²?
  24. 24.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the smallest whole number by which 250 must be divided to get a perfect square?
  28. 28.What is 86²? =
  29. 29.What is 32²? =
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  31. 31.Which of these is a perfect square? (a) 446 (b) 453 (c) 441
  32. 32.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is 22²? =
  34. 34.What is √7921? =
  35. 35.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  36. 36.What is √3249? =
  37. 37.Which of these is a perfect square? (a) 575 (b) 529 (c) 554
  38. 38.How many whole numbers lie between 21² and 22²?
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  40. 40.Which of these is a perfect square? (a) 252 (b) 225 (c) 253

Answer key

  1. 1296
  2. 1369
  3. 6084
  4. 361
  5. 2916
  6. 361
  7. 38
  8. 3600
  9. 77
  10. 45
  11. 88
  12. 1444
  13. 4225
  14. 25
  15. 70
  16. 62
  17. 47
  18. 46
  19. 784
  20. 68
  21. 169
  22. 1521
  23. 50
  24. 3
  25. 225
  26. 289
  27. 10
  28. 7396
  29. 1024
  30. 100
  31. 441
  32. 484
  33. 484
  34. 89
  35. 5
  36. 57
  37. 529
  38. 42
  39. 441
  40. 225

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