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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 199 · 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.A square garden has an area of 3481 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 113 (b) 114 (c) 100
  3. 3.What is the smallest whole number by which 243 must be divided to get a perfect square?
  4. 4.What is 71²? =
  5. 5.What is √5041? =
  6. 6.What is √2704? =
  7. 7.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  8. 8.What is 33²? =
  9. 9.How many whole numbers lie between 9² and 10²?
  10. 10.Which of these is a perfect square? (a) 149 (b) 168 (c) 144
  11. 11.Which of these is a perfect square? (a) 900 (b) 958 (c) 950
  12. 12.How many whole numbers lie between 20² and 21²?
  13. 13.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 37² and 38²?
  15. 15.How many whole numbers lie between 11² and 12²?
  16. 16.Which of these is a perfect square? (a) 766 (b) 729 (c) 731
  17. 17.Which of these is a perfect square? (a) 514 (b) 503 (c) 484
  18. 18.What is 24²? =
  19. 19.What is 61²? =
  20. 20.Which of these is a perfect square? (a) 261 (b) 259 (c) 256
  21. 21.How many whole numbers lie between 23² and 24²?
  22. 22.A square garden has an area of 1764 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 884 (b) 844 (c) 841
  24. 24.Which of these is a perfect square? (a) 1024 (b) 1038 (c) 1050
  25. 25.How many whole numbers lie between 38² and 39²?
  26. 26.What is the smallest whole number by which 640 must be divided to get a perfect square?
  27. 27.What is √169? =
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 2401 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 18² and 19²?
  32. 32.A square garden has an area of 2025 square m. How long is each side (in m)?
  33. 33.Which of these is a perfect square? (a) 184 (b) 169 (c) 187
  34. 34.A square garden has an area of 81 square m. How long is each side (in m)?
  35. 35.What is 36²? =
  36. 36.What is √784? =
  37. 37.What is 72²? =
  38. 38.How many whole numbers lie between 12² and 13²?
  39. 39.What is 37²? =
  40. 40.What is 95²? =

Answer key

  1. 59
  2. 100
  3. 3
  4. 5041
  5. 71
  6. 52
  7. 11
  8. 1089
  9. 18
  10. 144
  11. 900
  12. 40
  13. 169
  14. 74
  15. 22
  16. 729
  17. 484
  18. 576
  19. 3721
  20. 256
  21. 46
  22. 42
  23. 841
  24. 1024
  25. 76
  26. 10
  27. 13
  28. 100
  29. 49
  30. 5
  31. 36
  32. 45
  33. 169
  34. 9
  35. 1296
  36. 28
  37. 5184
  38. 24
  39. 1369
  40. 9025

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