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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 462 · 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) 784 (b) 820 (c) 810
  2. 2.How many whole numbers lie between 41² and 42²?
  3. 3.What is √1369? =
  4. 4.What is √1225? =
  5. 5.What is √4624? =
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the smallest whole number by which 125 must be divided to get a perfect square?
  8. 8.What is √4761? =
  9. 9.What is the smallest whole number by which 54 must be divided to get a perfect square?
  10. 10.What is √3844? =
  11. 11.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √361? =
  13. 13.How many whole numbers lie between 30² and 31²?
  14. 14.What is the smallest whole number by which 32 must be divided to get a perfect square?
  15. 15.What is √8100? =
  16. 16.What is √2916? =
  17. 17.What is the smallest whole number by which 252 must be divided to get a perfect square?
  18. 18.A square garden has an area of 1936 square m. How long is each side (in m)?
  19. 19.What is √9604? =
  20. 20.How many whole numbers lie between 15² and 16²?
  21. 21.How many whole numbers lie between 16² and 17²?
  22. 22.How many whole numbers lie between 12² and 13²?
  23. 23.How many whole numbers lie between 40² and 41²?
  24. 24.What is 35²? =
  25. 25.What is 70²? =
  26. 26.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1296 square m. How long is each side (in m)?
  28. 28.Which of these is a perfect square? (a) 491 (b) 484 (c) 517
  29. 29.A square garden has an area of 49 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is 48²? =
  32. 32.A square garden has an area of 3364 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 39² and 40²?
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is √6724? =
  37. 37.Which of these is a perfect square? (a) 233 (b) 225 (c) 232
  38. 38.What is 12²? =
  39. 39.What is √1296? =
  40. 40.What is the smallest whole number by which 640 must be multiplied to get a perfect square?

Answer key

  1. 784
  2. 82
  3. 37
  4. 35
  5. 68
  6. 289
  7. 5
  8. 69
  9. 6
  10. 62
  11. 324
  12. 19
  13. 60
  14. 2
  15. 90
  16. 54
  17. 7
  18. 44
  19. 98
  20. 30
  21. 32
  22. 24
  23. 80
  24. 1225
  25. 4900
  26. 361
  27. 36
  28. 484
  29. 7
  30. 100
  31. 2304
  32. 58
  33. 900
  34. 78
  35. 196
  36. 82
  37. 225
  38. 144
  39. 36
  40. 10

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