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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 35 · 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 1369 square m. How long is each side (in m)?
  2. 2.How many whole numbers lie between 15² and 16²?
  3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 625 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 100 (b) 106 (c) 102
  7. 7.A square garden has an area of 81 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 40 must be divided to get a perfect square?
  11. 11.A square garden has an area of 2704 square m. How long is each side (in m)?
  12. 12.What is √3969? =
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 828 (b) 800 (c) 784
  15. 15.What is the smallest whole number by which 27 must be divided to get a perfect square?
  16. 16.A square garden has an area of 441 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  18. 18.How many whole numbers lie between 50² and 51²?
  19. 19.How many whole numbers lie between 40² and 41²?
  20. 20.What is 56²? =
  21. 21.How many whole numbers lie between 36² and 37²?
  22. 22.What is √729? =
  23. 23.What is √7225? =
  24. 24.How many whole numbers lie between 45² and 46²?
  25. 25.Which of these is a perfect square? (a) 236 (b) 225 (c) 227
  26. 26.What is √256? =
  27. 27.Which of these is a perfect square? (a) 631 (b) 637 (c) 625
  28. 28.How many whole numbers lie between 22² and 23²?
  29. 29.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  31. 31.What is √6241? =
  32. 32.What is the smallest whole number by which 12 must be divided to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 188 (b) 169 (c) 172
  34. 34.What is the smallest whole number by which 44 must be divided to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 752 (b) 778 (c) 729
  36. 36.How many whole numbers lie between 9² and 10²?
  37. 37.What is 99²? =
  38. 38.What is √3844? =
  39. 39.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  40. 40.How many whole numbers lie between 35² and 36²?

Answer key

  1. 37
  2. 30
  3. 484
  4. 25
  5. 13
  6. 100
  7. 9
  8. 36
  9. 400
  10. 10
  11. 52
  12. 63
  13. 841
  14. 784
  15. 3
  16. 21
  17. 576
  18. 100
  19. 80
  20. 3136
  21. 72
  22. 27
  23. 85
  24. 90
  25. 225
  26. 16
  27. 625
  28. 44
  29. 361
  30. 13
  31. 79
  32. 3
  33. 169
  34. 11
  35. 729
  36. 18
  37. 9801
  38. 62
  39. 2
  40. 70

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