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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 593 · 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.A square garden has an area of 1024 square m. How long is each side (in m)?
  2. 2.What is 60²? =
  3. 3.Which of these is a perfect square? (a) 115 (b) 119 (c) 100
  4. 4.What is 25²? =
  5. 5.What is the smallest whole number by which 98 must be divided to get a perfect square?
  6. 6.How many whole numbers lie between 29² and 30²?
  7. 7.Which of these is a perfect square? (a) 196 (b) 204 (c) 211
  8. 8.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  9. 9.How many whole numbers lie between 7² and 8²?
  10. 10.Which of these is a perfect square? (a) 1036 (b) 1046 (c) 1024
  11. 11.How many whole numbers lie between 32² and 33²?
  12. 12.A square garden has an area of 2500 square m. How long is each side (in m)?
  13. 13.What is √8281? =
  14. 14.How many whole numbers lie between 5² and 6²?
  15. 15.What is √8649? =
  16. 16.Which of these is a perfect square? (a) 121 (b) 122 (c) 132
  17. 17.What is 30²? =
  18. 18.How many whole numbers lie between 20² and 21²?
  19. 19.What is 33²? =
  20. 20.What is the smallest whole number by which 252 must be divided to get a perfect square?
  21. 21.What is 97²? =
  22. 22.Which of these is a perfect square? (a) 347 (b) 324 (c) 360
  23. 23.What is 86²? =
  24. 24.What is √6724? =
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 56²? =
  27. 27.What is √6241? =
  28. 28.What is 62²? =
  29. 29.What is the smallest whole number by which 240 must be divided to get a perfect square?
  30. 30.How many whole numbers lie between 12² and 13²?
  31. 31.How many whole numbers lie between 11² and 12²?
  32. 32.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  33. 33.What is √1369? =
  34. 34.What is 65²? =
  35. 35.Which of these is a perfect square? (a) 1675 (b) 1635 (c) 1600
  36. 36.What is 93²? =
  37. 37.What is 96²? =
  38. 38.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  40. 40.A square garden has an area of 2401 square m. How long is each side (in m)?

Answer key

  1. 32
  2. 3600
  3. 100
  4. 625
  5. 2
  6. 58
  7. 196
  8. 6
  9. 14
  10. 1024
  11. 64
  12. 50
  13. 91
  14. 10
  15. 93
  16. 121
  17. 900
  18. 40
  19. 1089
  20. 7
  21. 9409
  22. 324
  23. 7396
  24. 82
  25. 441
  26. 3136
  27. 79
  28. 3844
  29. 15
  30. 24
  31. 22
  32. 7
  33. 37
  34. 4225
  35. 1600
  36. 8649
  37. 9216
  38. 64
  39. 81
  40. 49

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