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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 221 · 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 13²? =
  2. 2.What is √225? =
  3. 3.What is the smallest whole number by which 735 must be divided to get a perfect square?
  4. 4.What is √1089? =
  5. 5.How many whole numbers lie between 40² and 41²?
  6. 6.What is the smallest whole number by which 50 must be divided to get a perfect square?
  7. 7.What is √3481? =
  8. 8.What is 95²? =
  9. 9.What is 60²? =
  10. 10.A square garden has an area of 3136 square m. How long is each side (in m)?
  11. 11.What is 50²? =
  12. 12.What is 23²? =
  13. 13.A square garden has an area of 729 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 96 must be divided to get a perfect square?
  15. 15.What is √5329? =
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 49² and 50²?
  18. 18.Which of these is a perfect square? (a) 327 (b) 350 (c) 324
  19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  20. 20.How many whole numbers lie between 50² and 51²?
  21. 21.What is √169? =
  22. 22.A square garden has an area of 1024 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 256 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  25. 25.What is √4900? =
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 144 square m. How long is each side (in m)?
  28. 28.What is √1369? =
  29. 29.What is √1156? =
  30. 30.What is √1849? =
  31. 31.Which of these is a perfect square? (a) 874 (b) 841 (c) 889
  32. 32.What is 77²? =
  33. 33.Which of these is a perfect square? (a) 165 (b) 144 (c) 150
  34. 34.What is 28²? =
  35. 35.What is 15²? =
  36. 36.How many whole numbers lie between 11² and 12²?
  37. 37.Which of these is a perfect square? (a) 761 (b) 729 (c) 779
  38. 38.What is 54²? =
  39. 39.Which of these is a perfect square? (a) 1407 (b) 1369 (c) 1401
  40. 40.What is √8836? =

Answer key

  1. 169
  2. 15
  3. 15
  4. 33
  5. 80
  6. 2
  7. 59
  8. 9025
  9. 3600
  10. 56
  11. 2500
  12. 529
  13. 27
  14. 6
  15. 73
  16. 81
  17. 98
  18. 324
  19. 49
  20. 100
  21. 13
  22. 32
  23. 16
  24. 15
  25. 70
  26. 256
  27. 12
  28. 37
  29. 34
  30. 43
  31. 841
  32. 5929
  33. 144
  34. 784
  35. 225
  36. 22
  37. 729
  38. 2916
  39. 1369
  40. 94

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