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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 291 · 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 34²? =
  2. 2.A square garden has an area of 2116 square m. How long is each side (in m)?
  3. 3.Which of these is a perfect square? (a) 196 (b) 217 (c) 209
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √8464? =
  6. 6.What is 87²? =
  7. 7.What is the smallest whole number by which 245 must be divided to get a perfect square?
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 1024 square m. How long is each side (in m)?
  10. 10.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  11. 11.How many whole numbers lie between 45² and 46²?
  12. 12.How many whole numbers lie between 48² and 49²?
  13. 13.How many whole numbers lie between 34² and 35²?
  14. 14.A square garden has an area of 1089 square m. How long is each side (in m)?
  15. 15.What is 64²? =
  16. 16.What is 11²? =
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  18. 18.Which of these is a perfect square? (a) 1025 (b) 1024 (c) 1047
  19. 19.How many whole numbers lie between 7² and 8²?
  20. 20.A square garden has an area of 256 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 1296 (b) 1364 (c) 1349
  22. 22.Which of these is a perfect square? (a) 235 (b) 225 (c) 232
  23. 23.Which of these is a perfect square? (a) 284 (b) 256 (c) 259
  24. 24.What is 33²? =
  25. 25.Which of these is a perfect square? (a) 784 (b) 816 (c) 786
  26. 26.Which of these is a perfect square? (a) 611 (b) 576 (c) 598
  27. 27.What is √4356? =
  28. 28.How many whole numbers lie between 13² and 14²?
  29. 29.What is √8100? =
  30. 30.What is √2704? =
  31. 31.What is 62²? =
  32. 32.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  33. 33.What is 46²? =
  34. 34.What is 13²? =
  35. 35.What is √3136? =
  36. 36.How many whole numbers lie between 26² and 27²?
  37. 37.A square garden has an area of 289 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 484 (b) 519 (c) 503
  39. 39.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 72 must be multiplied to get a perfect square?

Answer key

  1. 1156
  2. 46
  3. 196
  4. 25
  5. 92
  6. 7569
  7. 5
  8. 36
  9. 32
  10. 900
  11. 90
  12. 96
  13. 68
  14. 33
  15. 4096
  16. 121
  17. 121
  18. 1024
  19. 14
  20. 16
  21. 1296
  22. 225
  23. 256
  24. 1089
  25. 784
  26. 576
  27. 66
  28. 26
  29. 90
  30. 52
  31. 3844
  32. 7
  33. 2116
  34. 169
  35. 56
  36. 52
  37. 17
  38. 484
  39. 529
  40. 2

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