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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 81 · 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) 974 (b) 961 (c) 995
  2. 2.A square garden has an area of 625 square m. How long is each side (in m)?
  3. 3.What is √3721? =
  4. 4.What is √9216? =
  5. 5.How many whole numbers lie between 29² and 30²?
  6. 6.A square garden has an area of 1444 square m. How long is each side (in m)?
  7. 7.What is 22²? =
  8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 69²? =
  10. 10.What is the smallest whole number by which 360 must be divided to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 484 (b) 489 (c) 493
  12. 12.A square garden has an area of 1296 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 214 (b) 196 (c) 199
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 13² and 14²?
  16. 16.Which of these is a perfect square? (a) 529 (b) 560 (c) 549
  17. 17.What is the smallest whole number by which 637 must be divided to get a perfect square?
  18. 18.How many whole numbers lie between 30² and 31²?
  19. 19.What is 64²? =
  20. 20.What is √5329? =
  21. 21.What is the smallest whole number by which 567 must be divided to get a perfect square?
  22. 22.What is √1296? =
  23. 23.Which of these is a perfect square? (a) 1185 (b) 1206 (c) 1156
  24. 24.What is 26²? =
  25. 25.A square garden has an area of 1225 square m. How long is each side (in m)?
  26. 26.What is √289? =
  27. 27.Which of these is a perfect square? (a) 297 (b) 290 (c) 289
  28. 28.A square garden has an area of 169 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 49 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  31. 31.Which of these is a perfect square? (a) 729 (b) 744 (c) 755
  32. 32.What is √400? =
  33. 33.Which of these is a perfect square? (a) 579 (b) 613 (c) 576
  34. 34.What is 63²? =
  35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  36. 36.How many whole numbers lie between 20² and 21²?
  37. 37.What is 43²? =
  38. 38.How many whole numbers lie between 12² and 13²?
  39. 39.Which of these is a perfect square? (a) 1024 (b) 1027 (c) 1058
  40. 40.What is the smallest whole number by which 18 must be multiplied to get a perfect square?

Answer key

  1. 961
  2. 25
  3. 61
  4. 96
  5. 58
  6. 38
  7. 484
  8. 324
  9. 4761
  10. 10
  11. 484
  12. 36
  13. 196
  14. 100
  15. 26
  16. 529
  17. 13
  18. 60
  19. 4096
  20. 73
  21. 7
  22. 36
  23. 1156
  24. 676
  25. 35
  26. 17
  27. 289
  28. 13
  29. 7
  30. 64
  31. 729
  32. 20
  33. 576
  34. 3969
  35. 484
  36. 40
  37. 1849
  38. 24
  39. 1024
  40. 2

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