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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 608 · 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 121 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 1273 (b) 1225 (c) 1231
  3. 3.Which of these is a perfect square? (a) 328 (b) 324 (c) 352
  4. 4.Which of these is a perfect square? (a) 363 (b) 385 (c) 361
  5. 5.A square garden has an area of 1225 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 1217 (b) 1157 (c) 1156
  7. 7.A square garden has an area of 529 square m. How long is each side (in m)?
  8. 8.What is √1089? =
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 43²? =
  11. 11.What is √7225? =
  12. 12.Which of these is a perfect square? (a) 144 (b) 160 (c) 165
  13. 13.How many whole numbers lie between 15² and 16²?
  14. 14.What is the smallest whole number by which 28 must be divided to get a perfect square?
  15. 15.A square garden has an area of 784 square m. How long is each side (in m)?
  16. 16.What is 93²? =
  17. 17.Which of these is a perfect square? (a) 1155 (b) 1143 (c) 1089
  18. 18.A square garden has an area of 49 square m. How long is each side (in m)?
  19. 19.How many whole numbers lie between 38² and 39²?
  20. 20.A square garden has an area of 2809 square m. How long is each side (in m)?
  21. 21.What is 65²? =
  22. 22.What is √2601? =
  23. 23.What is 69²? =
  24. 24.How many whole numbers lie between 49² and 50²?
  25. 25.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  27. 27.What is √400? =
  28. 28.What is the smallest whole number by which 375 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 46² and 47²?
  30. 30.Which of these is a perfect square? (a) 996 (b) 988 (c) 961
  31. 31.How many whole numbers lie between 18² and 19²?
  32. 32.What is √8281? =
  33. 33.A square garden has an area of 2500 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the smallest whole number by which 75 must be divided to get a perfect square?
  36. 36.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  37. 37.How many whole numbers lie between 19² and 20²?
  38. 38.What is 19²? =
  39. 39.Which of these is a perfect square? (a) 900 (b) 914 (c) 929
  40. 40.How many whole numbers lie between 44² and 45²?

Answer key

  1. 11
  2. 1225
  3. 324
  4. 361
  5. 35
  6. 1156
  7. 23
  8. 33
  9. 256
  10. 1849
  11. 85
  12. 144
  13. 30
  14. 7
  15. 28
  16. 8649
  17. 1089
  18. 7
  19. 76
  20. 53
  21. 4225
  22. 51
  23. 4761
  24. 98
  25. 7
  26. 6
  27. 20
  28. 15
  29. 92
  30. 961
  31. 36
  32. 91
  33. 50
  34. 49
  35. 3
  36. 10
  37. 38
  38. 361
  39. 900
  40. 88

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