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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 502 · 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 1089 square m. How long is each side (in m)?
  2. 2.What is √6084? =
  3. 3.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  4. 4.Which of these is a perfect square? (a) 290 (b) 300 (c) 289
  5. 5.A square garden has an area of 3136 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 230 (b) 239 (c) 225
  7. 7.How many whole numbers lie between 50² and 51²?
  8. 8.What is 59²? =
  9. 9.A square garden has an area of 361 square m. How long is each side (in m)?
  10. 10.What is √4624? =
  11. 11.Which of these is a perfect square? (a) 1068 (b) 1024 (c) 1045
  12. 12.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  13. 13.What is the smallest whole number by which 343 must be divided to get a perfect square?
  14. 14.What is √289? =
  15. 15.How many whole numbers lie between 6² and 7²?
  16. 16.Which of these is a perfect square? (a) 351 (b) 354 (c) 324
  17. 17.Which of these is a perfect square? (a) 833 (b) 784 (c) 830
  18. 18.Which of these is a perfect square? (a) 549 (b) 571 (c) 529
  19. 19.What is √361? =
  20. 20.A square garden has an area of 784 square m. How long is each side (in m)?
  21. 21.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √6889? =
  23. 23.What is √729? =
  24. 24.What is 69²? =
  25. 25.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  26. 26.What is √5184? =
  27. 27.Which of these is a perfect square? (a) 1264 (b) 1225 (c) 1243
  28. 28.How many whole numbers lie between 40² and 41²?
  29. 29.What is √6561? =
  30. 30.What is the smallest whole number by which 72 must be divided to get a perfect square?
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 49² and 50²?
  33. 33.Which of these is a perfect square? (a) 256 (b) 288 (c) 262
  34. 34.How many whole numbers lie between 14² and 15²?
  35. 35.How many whole numbers lie between 11² and 12²?
  36. 36.What is 13²? =
  37. 37.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is 40²? =
  39. 39.How many whole numbers lie between 22² and 23²?
  40. 40.What is 25²? =

Answer key

  1. 33
  2. 78
  3. 900
  4. 289
  5. 56
  6. 225
  7. 100
  8. 3481
  9. 19
  10. 68
  11. 1024
  12. 11
  13. 7
  14. 17
  15. 12
  16. 324
  17. 784
  18. 529
  19. 19
  20. 28
  21. 324
  22. 83
  23. 27
  24. 4761
  25. 10
  26. 72
  27. 1225
  28. 80
  29. 81
  30. 2
  31. 121
  32. 98
  33. 256
  34. 28
  35. 22
  36. 169
  37. 225
  38. 1600
  39. 44
  40. 625

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