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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 342 · 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.A square garden has an area of 2304 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 121 (b) 143 (c) 135
  4. 4.What is √4096? =
  5. 5.What is 56²? =
  6. 6.What is 65²? =
  7. 7.How many whole numbers lie between 24² and 25²?
  8. 8.What is 97²? =
  9. 9.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √8100? =
  11. 11.Which of these is a perfect square? (a) 238 (b) 225 (c) 228
  12. 12.A square garden has an area of 441 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 630 (b) 625 (c) 647
  14. 14.How many whole numbers lie between 50² and 51²?
  15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  16. 16.Which of these is a perfect square? (a) 200 (b) 199 (c) 196
  17. 17.How many whole numbers lie between 8² and 9²?
  18. 18.A square garden has an area of 1600 square m. How long is each side (in m)?
  19. 19.What is √2916? =
  20. 20.Which of these is a perfect square? (a) 1412 (b) 1379 (c) 1369
  21. 21.What is √4761? =
  22. 22.What is 17²? =
  23. 23.What is the smallest whole number by which 245 must be divided to get a perfect square?
  24. 24.What is √7744? =
  25. 25.A square garden has an area of 3600 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √4356? =
  29. 29.What is √3844? =
  30. 30.Which of these is a perfect square? (a) 1034 (b) 1062 (c) 1024
  31. 31.What is 80²? =
  32. 32.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  33. 33.A square garden has an area of 1369 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 15² and 16²?
  35. 35.Which of these is a perfect square? (a) 842 (b) 841 (c) 843
  36. 36.How many whole numbers lie between 41² and 42²?
  37. 37.How many whole numbers lie between 27² and 28²?
  38. 38.What is √5776? =
  39. 39.A square garden has an area of 1681 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 18² and 19²?

Answer key

  1. 48
  2. 169
  3. 121
  4. 64
  5. 3136
  6. 4225
  7. 48
  8. 9409
  9. 361
  10. 90
  11. 225
  12. 21
  13. 625
  14. 100
  15. 81
  16. 196
  17. 16
  18. 40
  19. 54
  20. 1369
  21. 69
  22. 289
  23. 5
  24. 88
  25. 60
  26. 225
  27. 784
  28. 66
  29. 62
  30. 1024
  31. 6400
  32. 13
  33. 37
  34. 30
  35. 841
  36. 82
  37. 54
  38. 76
  39. 41
  40. 36

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