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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 526 · 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 28²? =
  2. 2.Which of these is a perfect square? (a) 670 (b) 625 (c) 643
  3. 3.What is √4356? =
  4. 4.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is 94²? =
  7. 7.Which of these is a perfect square? (a) 1348 (b) 1313 (c) 1296
  8. 8.What is √1849? =
  9. 9.What is 27²? =
  10. 10.How many whole numbers lie between 17² and 18²?
  11. 11.Which of these is a perfect square? (a) 1401 (b) 1372 (c) 1369
  12. 12.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  13. 13.Which of these is a perfect square? (a) 376 (b) 361 (c) 377
  14. 14.Which of these is a perfect square? (a) 1545 (b) 1533 (c) 1521
  15. 15.What is the smallest whole number by which 63 must be divided to get a perfect square?
  16. 16.What is 37²? =
  17. 17.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  18. 18.Which of these is a perfect square? (a) 1024 (b) 1058 (c) 1042
  19. 19.What is 46²? =
  20. 20.A square garden has an area of 1225 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 420 (b) 400 (c) 415
  22. 22.Which of these is a perfect square? (a) 289 (b) 313 (c) 294
  23. 23.What is 15²? =
  24. 24.Which of these is a perfect square? (a) 169 (b) 194 (c) 189
  25. 25.A square garden has an area of 1156 square m. How long is each side (in m)?
  26. 26.What is 24²? =
  27. 27.How many whole numbers lie between 35² and 36²?
  28. 28.Which of these is a perfect square? (a) 568 (b) 531 (c) 529
  29. 29.What is 84²? =
  30. 30.What is 73²? =
  31. 31.A square garden has an area of 3364 square m. How long is each side (in m)?
  32. 32.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 7² and 8²?
  34. 34.What is 26²? =
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 228 (b) 239 (c) 225
  37. 37.What is √6889? =
  38. 38.What is 57²? =
  39. 39.A square garden has an area of 784 square m. How long is each side (in m)?
  40. 40.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 784
  2. 625
  3. 66
  4. 3
  5. 361
  6. 8836
  7. 1296
  8. 43
  9. 729
  10. 34
  11. 1369
  12. 15
  13. 361
  14. 1521
  15. 7
  16. 1369
  17. 784
  18. 1024
  19. 2116
  20. 35
  21. 400
  22. 289
  23. 225
  24. 169
  25. 34
  26. 576
  27. 70
  28. 529
  29. 7056
  30. 5329
  31. 58
  32. 36
  33. 14
  34. 676
  35. 100
  36. 225
  37. 83
  38. 3249
  39. 28
  40. 256

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