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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 693 · 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 √6724? =
  2. 2.What is √324? =
  3. 3.What is √361? =
  4. 4.What is √5929? =
  5. 5.How many whole numbers lie between 44² and 45²?
  6. 6.A square garden has an area of 625 square m. How long is each side (in m)?
  7. 7.How many whole numbers lie between 6² and 7²?
  8. 8.What is 13²? =
  9. 9.How many whole numbers lie between 5² and 6²?
  10. 10.What is 53²? =
  11. 11.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  12. 12.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  13. 13.A square garden has an area of 36 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  15. 15.What is 50²? =
  16. 16.A square garden has an area of 169 square m. How long is each side (in m)?
  17. 17.What is 40²? =
  18. 18.How many whole numbers lie between 33² and 34²?
  19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  20. 20.A square garden has an area of 3600 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 10² and 11²?
  22. 22.Which of these is a perfect square? (a) 139 (b) 121 (c) 134
  23. 23.How many whole numbers lie between 18² and 19²?
  24. 24.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  25. 25.What is the smallest whole number by which 216 must be divided to get a perfect square?
  26. 26.What is 73²? =
  27. 27.A square garden has an area of 2916 square m. How long is each side (in m)?
  28. 28.Which of these is a perfect square? (a) 908 (b) 951 (c) 900
  29. 29.What is 64²? =
  30. 30.What is 49²? =
  31. 31.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  32. 32.How many whole numbers lie between 15² and 16²?
  33. 33.A square garden has an area of 400 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 24² and 25²?
  35. 35.Which of these is a perfect square? (a) 1344 (b) 1319 (c) 1296
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 3136 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 881 (b) 841 (c) 856
  39. 39.Which of these is a perfect square? (a) 1257 (b) 1234 (c) 1225
  40. 40.What is √2809? =

Answer key

  1. 82
  2. 18
  3. 19
  4. 77
  5. 88
  6. 25
  7. 12
  8. 169
  9. 10
  10. 2809
  11. 7
  12. 5
  13. 6
  14. 11
  15. 2500
  16. 13
  17. 1600
  18. 66
  19. 196
  20. 60
  21. 20
  22. 121
  23. 36
  24. 7
  25. 6
  26. 5329
  27. 54
  28. 900
  29. 4096
  30. 2401
  31. 14
  32. 30
  33. 20
  34. 48
  35. 1296
  36. 100
  37. 56
  38. 841
  39. 1225
  40. 53

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