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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 542 · 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) 226 (b) 234 (c) 225
  2. 2.What is √289? =
  3. 3.A square garden has an area of 324 square m. How long is each side (in m)?
  4. 4.What is 42²? =
  5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  6. 6.Which of these is a perfect square? (a) 692 (b) 676 (c) 696
  7. 7.How many whole numbers lie between 43² and 44²?
  8. 8.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  9. 9.What is 27²? =
  10. 10.What is 46²? =
  11. 11.How many whole numbers lie between 6² and 7²?
  12. 12.What is the smallest whole number by which 98 must be divided to get a perfect square?
  13. 13.What is 77²? =
  14. 14.A square garden has an area of 256 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 240 must be divided to get a perfect square?
  16. 16.A square garden has an area of 3481 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 3025 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 34² and 35²?
  19. 19.A square garden has an area of 2916 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 1444 (b) 1485 (c) 1471
  21. 21.Which of these is a perfect square? (a) 457 (b) 441 (c) 473
  22. 22.A square garden has an area of 2116 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 1167 (b) 1187 (c) 1156
  24. 24.What is 23²? =
  25. 25.What is 63²? =
  26. 26.What is √2025? =
  27. 27.How many whole numbers lie between 37² and 38²?
  28. 28.What is the smallest whole number by which 60 must be divided to get a perfect square?
  29. 29.A square garden has an area of 2304 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 2209 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  32. 32.A square garden has an area of 3136 square m. How long is each side (in m)?
  33. 33.What is √1225? =
  34. 34.What is √6724? =
  35. 35.How many whole numbers lie between 14² and 15²?
  36. 36.How many whole numbers lie between 50² and 51²?
  37. 37.What is 96²? =
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √400? =
  40. 40.What is √484? =

Answer key

  1. 225
  2. 17
  3. 18
  4. 1764
  5. 144
  6. 676
  7. 86
  8. 13
  9. 729
  10. 2116
  11. 12
  12. 2
  13. 5929
  14. 16
  15. 15
  16. 59
  17. 55
  18. 68
  19. 54
  20. 1444
  21. 441
  22. 46
  23. 1156
  24. 529
  25. 3969
  26. 45
  27. 74
  28. 15
  29. 48
  30. 47
  31. 361
  32. 56
  33. 35
  34. 82
  35. 28
  36. 100
  37. 9216
  38. 400
  39. 20
  40. 22

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