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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 387 · 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 17² and 18²?
  2. 2.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 1318 (b) 1296 (c) 1345
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √3364? =
  6. 6.Which of these is a perfect square? (a) 1264 (b) 1225 (c) 1287
  7. 7.What is the smallest whole number by which 98 must be divided to get a perfect square?
  8. 8.What is 92²? =
  9. 9.What is 94²? =
  10. 10.A square garden has an area of 1764 square m. How long is each side (in m)?
  11. 11.What is √2500? =
  12. 12.Which of these is a perfect square? (a) 539 (b) 529 (c) 557
  13. 13.What is √2209? =
  14. 14.How many whole numbers lie between 31² and 32²?
  15. 15.Which of these is a perfect square? (a) 443 (b) 441 (c) 444
  16. 16.What is √9025? =
  17. 17.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  18. 18.What is √576? =
  19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  20. 20.Which of these is a perfect square? (a) 411 (b) 400 (c) 425
  21. 21.Which of these is a perfect square? (a) 881 (b) 841 (c) 896
  22. 22.What is the smallest whole number by which 24 must be divided to get a perfect square?
  23. 23.What is 53²? =
  24. 24.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 250 must be divided to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 904 (b) 910 (c) 900
  28. 28.What is 73²? =
  29. 29.Which of these is a perfect square? (a) 289 (b) 306 (c) 296
  30. 30.How many whole numbers lie between 8² and 9²?
  31. 31.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 806 (b) 819 (c) 784
  33. 33.A square garden has an area of 2809 square m. How long is each side (in m)?
  34. 34.What is √1369? =
  35. 35.A square garden has an area of 1849 square m. How long is each side (in m)?
  36. 36.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  37. 37.What is √676? =
  38. 38.What is √900? =
  39. 39.How many whole numbers lie between 15² and 16²?
  40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 34
  2. 3
  3. 1296
  4. 25
  5. 58
  6. 1225
  7. 2
  8. 8464
  9. 8836
  10. 42
  11. 50
  12. 529
  13. 47
  14. 62
  15. 441
  16. 95
  17. 5
  18. 24
  19. 49
  20. 400
  21. 841
  22. 6
  23. 2809
  24. 361
  25. 10
  26. 10
  27. 900
  28. 5329
  29. 289
  30. 16
  31. 13
  32. 784
  33. 53
  34. 37
  35. 43
  36. 6
  37. 26
  38. 30
  39. 30
  40. 676

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