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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 666 · 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 the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the smallest whole number by which 468 must be divided to get a perfect square?
  3. 3.What is √2401? =
  4. 4.What is √625? =
  5. 5.What is the smallest whole number by which 45 must be divided to get a perfect square?
  6. 6.What is 80²? =
  7. 7.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 67²? =
  9. 9.What is 39²? =
  10. 10.What is 54²? =
  11. 11.What is √1681? =
  12. 12.What is 79²? =
  13. 13.What is 94²? =
  14. 14.A square garden has an area of 529 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 324 (b) 345 (c) 333
  16. 16.Which of these is a perfect square? (a) 1054 (b) 1024 (c) 1082
  17. 17.What is √121? =
  18. 18.How many whole numbers lie between 15² and 16²?
  19. 19.What is the smallest whole number by which 150 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 50 must be divided to get a perfect square?
  21. 21.What is √784? =
  22. 22.What is √1600? =
  23. 23.What is 37²? =
  24. 24.Which of these is a perfect square? (a) 529 (b) 574 (c) 532
  25. 25.Which of these is a perfect square? (a) 513 (b) 484 (c) 492
  26. 26.What is 61²? =
  27. 27.What is √1156? =
  28. 28.What is √2209? =
  29. 29.What is √3136? =
  30. 30.How many whole numbers lie between 22² and 23²?
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √5041? =
  33. 33.What is √5184? =
  34. 34.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  35. 35.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  36. 36.How many whole numbers lie between 10² and 11²?
  37. 37.What is 28²? =
  38. 38.What is √676? =
  39. 39.What is 34²? =
  40. 40.What is the smallest whole number by which 112 must be divided to get a perfect square?

Answer key

  1. 36
  2. 13
  3. 49
  4. 25
  5. 5
  6. 6400
  7. 144
  8. 4489
  9. 1521
  10. 2916
  11. 41
  12. 6241
  13. 8836
  14. 23
  15. 324
  16. 1024
  17. 11
  18. 30
  19. 6
  20. 2
  21. 28
  22. 40
  23. 1369
  24. 529
  25. 484
  26. 3721
  27. 34
  28. 47
  29. 56
  30. 44
  31. 64
  32. 71
  33. 72
  34. 2
  35. 11
  36. 20
  37. 784
  38. 26
  39. 1156
  40. 7

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