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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 432 · 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 √7744? =
  2. 2.What is √1225? =
  3. 3.Which of these is a perfect square? (a) 127 (b) 121 (c) 132
  4. 4.Which of these is a perfect square? (a) 371 (b) 392 (c) 361
  5. 5.How many whole numbers lie between 41² and 42²?
  6. 6.What is √4900? =
  7. 7.Which of these is a perfect square? (a) 1444 (b) 1499 (c) 1489
  8. 8.What is 42²? =
  9. 9.What is √324? =
  10. 10.Which of these is a perfect square? (a) 327 (b) 324 (c) 326
  11. 11.What is 16²? =
  12. 12.Which of these is a perfect square? (a) 771 (b) 729 (c) 746
  13. 13.What is the smallest whole number by which 28 must be divided to get a perfect square?
  14. 14.A square garden has an area of 2401 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 45 must be divided to get a perfect square?
  16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √2601? =
  18. 18.Which of these is a perfect square? (a) 1049 (b) 1032 (c) 1024
  19. 19.Which of these is a perfect square? (a) 676 (b) 677 (c) 695
  20. 20.How many whole numbers lie between 16² and 17²?
  21. 21.Which of these is a perfect square? (a) 961 (b) 1007 (c) 1005
  22. 22.A square garden has an area of 361 square m. How long is each side (in m)?
  23. 23.What is √1369? =
  24. 24.A square garden has an area of 400 square m. How long is each side (in m)?
  25. 25.What is 93²? =
  26. 26.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  27. 27.How many whole numbers lie between 44² and 45²?
  28. 28.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is 50²? =
  31. 31.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √7396? =
  33. 33.How many whole numbers lie between 10² and 11²?
  34. 34.How many whole numbers lie between 21² and 22²?
  35. 35.A square garden has an area of 1156 square m. How long is each side (in m)?
  36. 36.A square garden has an area of 64 square m. How long is each side (in m)?
  37. 37.A square garden has an area of 2500 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 1149 (b) 1147 (c) 1089
  39. 39.What is 70²? =
  40. 40.What is √289? =

Answer key

  1. 88
  2. 35
  3. 121
  4. 361
  5. 82
  6. 70
  7. 1444
  8. 1764
  9. 18
  10. 324
  11. 256
  12. 729
  13. 7
  14. 49
  15. 5
  16. 324
  17. 51
  18. 1024
  19. 676
  20. 32
  21. 961
  22. 19
  23. 37
  24. 20
  25. 8649
  26. 6
  27. 88
  28. 7
  29. 576
  30. 2500
  31. 225
  32. 86
  33. 20
  34. 42
  35. 34
  36. 8
  37. 50
  38. 1089
  39. 4900
  40. 17

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