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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 223 · 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.How many whole numbers lie between 31² and 32²?
  2. 2.How many whole numbers lie between 8² and 9²?
  3. 3.A square garden has an area of 1936 square m. How long is each side (in m)?
  4. 4.What is √2116? =
  5. 5.A square garden has an area of 1849 square m. How long is each side (in m)?
  6. 6.What is √6889? =
  7. 7.A square garden has an area of 2916 square m. How long is each side (in m)?
  8. 8.A square garden has an area of 676 square m. How long is each side (in m)?
  9. 9.Which of these is a perfect square? (a) 100 (b) 101 (c) 120
  10. 10.Which of these is a perfect square? (a) 913 (b) 900 (c) 942
  11. 11.What is the smallest whole number by which 243 must be divided to get a perfect square?
  12. 12.A square garden has an area of 3249 square m. How long is each side (in m)?
  13. 13.What is √2916? =
  14. 14.Which of these is a perfect square? (a) 1411 (b) 1422 (c) 1369
  15. 15.What is 90²? =
  16. 16.A square garden has an area of 2025 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  18. 18.How many whole numbers lie between 45² and 46²?
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 16²? =
  21. 21.What is 53²? =
  22. 22.What is the smallest whole number by which 128 must be divided to get a perfect square?
  23. 23.What is 22²? =
  24. 24.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  25. 25.Which of these is a perfect square? (a) 1600 (b) 1618 (c) 1656
  26. 26.How many whole numbers lie between 46² and 47²?
  27. 27.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  28. 28.How many whole numbers lie between 12² and 13²?
  29. 29.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  30. 30.How many whole numbers lie between 36² and 37²?
  31. 31.What is 81²? =
  32. 32.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  33. 33.How many whole numbers lie between 44² and 45²?
  34. 34.A square garden has an area of 81 square m. How long is each side (in m)?
  35. 35.What is 32²? =
  36. 36.How many whole numbers lie between 48² and 49²?
  37. 37.What is √1936? =
  38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 1116 (b) 1089 (c) 1109
  40. 40.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 62
  2. 16
  3. 44
  4. 46
  5. 43
  6. 83
  7. 54
  8. 26
  9. 100
  10. 900
  11. 3
  12. 57
  13. 54
  14. 1369
  15. 8100
  16. 45
  17. 11
  18. 90
  19. 361
  20. 256
  21. 2809
  22. 2
  23. 484
  24. 484
  25. 1600
  26. 92
  27. 225
  28. 24
  29. 13
  30. 72
  31. 6561
  32. 3
  33. 88
  34. 9
  35. 1024
  36. 96
  37. 44
  38. 900
  39. 1089
  40. 529

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