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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 121 · 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.How many whole numbers lie between 5² and 6²?
  2. 2.A square garden has an area of 3136 square m. How long is each side (in m)?
  3. 3.How many whole numbers lie between 40² and 41²?
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 28² and 29²?
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √1849? =
  9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 67²? =
  11. 11.What is 12²? =
  12. 12.What is √1296? =
  13. 13.What is the smallest whole number by which 175 must be divided to get a perfect square?
  14. 14.How many whole numbers lie between 41² and 42²?
  15. 15.A square garden has an area of 1156 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 256 square m. How long is each side (in m)?
  17. 17.What is 74²? =
  18. 18.What is the smallest whole number by which 245 must be divided to get a perfect square?
  19. 19.What is √625? =
  20. 20.What is 49²? =
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  22. 22.How many whole numbers lie between 26² and 27²?
  23. 23.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √4096? =
  25. 25.A square garden has an area of 1089 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 227 (b) 241 (c) 225
  27. 27.A square garden has an area of 324 square m. How long is each side (in m)?
  28. 28.What is √121? =
  29. 29.A square garden has an area of 36 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 8 must be divided to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 749 (b) 734 (c) 729
  32. 32.A square garden has an area of 1849 square m. How long is each side (in m)?
  33. 33.What is √4900? =
  34. 34.What is 23²? =
  35. 35.What is the smallest whole number by which 50 must be divided to get a perfect square?
  36. 36.What is √1024? =
  37. 37.What is √900? =
  38. 38.What is √484? =
  39. 39.What is √3136? =
  40. 40.What is √1600? =

Answer key

  1. 10
  2. 56
  3. 80
  4. 196
  5. 56
  6. 64
  7. 784
  8. 43
  9. 529
  10. 4489
  11. 144
  12. 36
  13. 7
  14. 82
  15. 34
  16. 16
  17. 5476
  18. 5
  19. 25
  20. 2401
  21. 36
  22. 52
  23. 256
  24. 64
  25. 33
  26. 225
  27. 18
  28. 11
  29. 6
  30. 2
  31. 729
  32. 43
  33. 70
  34. 529
  35. 2
  36. 32
  37. 30
  38. 22
  39. 56
  40. 40

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