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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 377 · 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 50²? =
  2. 2.A square garden has an area of 225 square m. How long is each side (in m)?
  3. 3.Which of these is a perfect square? (a) 477 (b) 441 (c) 470
  4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 81 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  8. 8.What is 84²? =
  9. 9.A square garden has an area of 361 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 1093 (b) 1137 (c) 1089
  11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 1289 (b) 1225 (c) 1231
  13. 13.Which of these is a perfect square? (a) 947 (b) 900 (c) 949
  14. 14.A square garden has an area of 36 square m. How long is each side (in m)?
  15. 15.What is √4356? =
  16. 16.Which of these is a perfect square? (a) 1073 (b) 1070 (c) 1024
  17. 17.What is √1225? =
  18. 18.How many whole numbers lie between 29² and 30²?
  19. 19.What is 96²? =
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √8100? =
  22. 22.Which of these is a perfect square? (a) 361 (b) 393 (c) 398
  23. 23.What is 93²? =
  24. 24.What is 73²? =
  25. 25.What is 56²? =
  26. 26.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  27. 27.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  28. 28.How many whole numbers lie between 50² and 51²?
  29. 29.What is 15²? =
  30. 30.What is √6241? =
  31. 31.What is 49²? =
  32. 32.How many whole numbers lie between 13² and 14²?
  33. 33.What is √1849? =
  34. 34.What is 70²? =
  35. 35.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  36. 36.A square garden has an area of 1225 square m. How long is each side (in m)?
  37. 37.What is √2601? =
  38. 38.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 963 (b) 979 (c) 961
  40. 40.What is √7744? =

Answer key

  1. 2500
  2. 15
  3. 441
  4. 324
  5. 121
  6. 9
  7. 11
  8. 7056
  9. 19
  10. 1089
  11. 256
  12. 1225
  13. 900
  14. 6
  15. 66
  16. 1024
  17. 35
  18. 58
  19. 9216
  20. 81
  21. 90
  22. 361
  23. 8649
  24. 5329
  25. 3136
  26. 6
  27. 13
  28. 100
  29. 225
  30. 79
  31. 2401
  32. 26
  33. 43
  34. 4900
  35. 2
  36. 35
  37. 51
  38. 49
  39. 961
  40. 88

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