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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 685 · 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 √961? =
  2. 2.How many whole numbers lie between 21² and 22²?
  3. 3.What is √484? =
  4. 4.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  5. 5.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 44² and 45²?
  7. 7.What is √8100? =
  8. 8.How many whole numbers lie between 15² and 16²?
  9. 9.How many whole numbers lie between 16² and 17²?
  10. 10.Which of these is a perfect square? (a) 275 (b) 286 (c) 256
  11. 11.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 361 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 49 square m. How long is each side (in m)?
  15. 15.What is 44²? =
  16. 16.What is √1089? =
  17. 17.How many whole numbers lie between 48² and 49²?
  18. 18.How many whole numbers lie between 8² and 9²?
  19. 19.Which of these is a perfect square? (a) 936 (b) 927 (c) 900
  20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 663 (b) 635 (c) 625
  22. 22.How many whole numbers lie between 25² and 26²?
  23. 23.What is √4489? =
  24. 24.What is 86²? =
  25. 25.How many whole numbers lie between 41² and 42²?
  26. 26.How many whole numbers lie between 35² and 36²?
  27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √3136? =
  29. 29.A square garden has an area of 64 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √900? =
  32. 32.What is 70²? =
  33. 33.What is √9216? =
  34. 34.What is 90²? =
  35. 35.How many whole numbers lie between 7² and 8²?
  36. 36.What is √1225? =
  37. 37.What is 84²? =
  38. 38.Which of these is a perfect square? (a) 841 (b) 873 (c) 852
  39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  40. 40.Which of these is a perfect square? (a) 982 (b) 961 (c) 1016

Answer key

  1. 31
  2. 42
  3. 22
  4. 10
  5. 625
  6. 88
  7. 90
  8. 30
  9. 32
  10. 256
  11. 3
  12. 729
  13. 19
  14. 7
  15. 1936
  16. 33
  17. 96
  18. 16
  19. 900
  20. 441
  21. 625
  22. 50
  23. 67
  24. 7396
  25. 82
  26. 70
  27. 81
  28. 56
  29. 8
  30. 289
  31. 30
  32. 4900
  33. 96
  34. 8100
  35. 14
  36. 35
  37. 7056
  38. 841
  39. 64
  40. 961

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