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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 717 · 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 32²? =
  2. 2.Which of these is a perfect square? (a) 1156 (b) 1202 (c) 1170
  3. 3.What is √2809? =
  4. 4.Which of these is a perfect square? (a) 845 (b) 854 (c) 841
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √6400? =
  7. 7.How many whole numbers lie between 35² and 36²?
  8. 8.What is 93²? =
  9. 9.What is √2500? =
  10. 10.What is the smallest whole number by which 40 must be divided to get a perfect square?
  11. 11.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  12. 12.What is √2601? =
  13. 13.What is the smallest whole number by which 810 must be divided to get a perfect square?
  14. 14.What is 25²? =
  15. 15.Which of these is a perfect square? (a) 445 (b) 450 (c) 441
  16. 16.What is 31²? =
  17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is 28²? =
  19. 19.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 86²? =
  21. 21.Which of these is a perfect square? (a) 900 (b) 903 (c) 925
  22. 22.A square garden has an area of 2401 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 23² and 24²?
  24. 24.What is √5776? =
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 396 must be divided to get a perfect square?
  27. 27.What is 14²? =
  28. 28.What is √729? =
  29. 29.What is 76²? =
  30. 30.What is √1089? =
  31. 31.A square garden has an area of 100 square m. How long is each side (in m)?
  32. 32.What is √961? =
  33. 33.What is 54²? =
  34. 34.A square garden has an area of 324 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 1089 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 247 (b) 249 (c) 225
  37. 37.What is √400? =
  38. 38.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  39. 39.What is the smallest whole number by which 12 must be divided to get a perfect square?
  40. 40.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 1024
  2. 1156
  3. 53
  4. 841
  5. 49
  6. 80
  7. 70
  8. 8649
  9. 50
  10. 10
  11. 14
  12. 51
  13. 10
  14. 625
  15. 441
  16. 961
  17. 64
  18. 784
  19. 576
  20. 7396
  21. 900
  22. 49
  23. 46
  24. 76
  25. 100
  26. 11
  27. 196
  28. 27
  29. 5776
  30. 33
  31. 10
  32. 31
  33. 2916
  34. 18
  35. 33
  36. 225
  37. 20
  38. 3
  39. 3
  40. 361

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