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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 40 · 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.Which of these is a perfect square? (a) 256 (b) 269 (c) 271
  2. 2.How many whole numbers lie between 19² and 20²?
  3. 3.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √9801? =
  6. 6.Which of these is a perfect square? (a) 297 (b) 304 (c) 289
  7. 7.Which of these is a perfect square? (a) 964 (b) 1016 (c) 961
  8. 8.What is 33²? =
  9. 9.A square garden has an area of 144 square m. How long is each side (in m)?
  10. 10.What is √1521? =
  11. 11.What is √8836? =
  12. 12.How many whole numbers lie between 6² and 7²?
  13. 13.A square garden has an area of 576 square m. How long is each side (in m)?
  14. 14.What is 43²? =
  15. 15.How many whole numbers lie between 25² and 26²?
  16. 16.A square garden has an area of 1089 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 13² and 14²?
  18. 18.Which of these is a perfect square? (a) 131 (b) 124 (c) 121
  19. 19.How many whole numbers lie between 26² and 27²?
  20. 20.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 256 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 3481 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 529 square m. How long is each side (in m)?
  24. 24.Which of these is a perfect square? (a) 225 (b) 241 (c) 245
  25. 25.What is √1296? =
  26. 26.What is 68²? =
  27. 27.Which of these is a perfect square? (a) 487 (b) 518 (c) 484
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 784 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  31. 31.What is √6400? =
  32. 32.A square garden has an area of 1024 square m. How long is each side (in m)?
  33. 33.What is 40²? =
  34. 34.What is 63²? =
  35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 772 (b) 774 (c) 729
  37. 37.What is 84²? =
  38. 38.Which of these is a perfect square? (a) 398 (b) 368 (c) 361
  39. 39.A square garden has an area of 289 square m. How long is each side (in m)?
  40. 40.What is √6561? =

Answer key

  1. 256
  2. 38
  3. 2
  4. 784
  5. 99
  6. 289
  7. 961
  8. 1089
  9. 12
  10. 39
  11. 94
  12. 12
  13. 24
  14. 1849
  15. 50
  16. 33
  17. 26
  18. 121
  19. 52
  20. 14
  21. 16
  22. 59
  23. 23
  24. 225
  25. 36
  26. 4624
  27. 484
  28. 36
  29. 28
  30. 6
  31. 80
  32. 32
  33. 1600
  34. 3969
  35. 529
  36. 729
  37. 7056
  38. 361
  39. 17
  40. 81

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