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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 405 · 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 2209 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 703 (b) 676 (c) 686
  3. 3.What is 35²? =
  4. 4.What is the smallest whole number by which 54 must be divided to get a perfect square?
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  6. 6.Which of these is a perfect square? (a) 574 (b) 554 (c) 529
  7. 7.Which of these is a perfect square? (a) 177 (b) 169 (c) 193
  8. 8.How many whole numbers lie between 11² and 12²?
  9. 9.Which of these is a perfect square? (a) 196 (b) 210 (c) 216
  10. 10.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  11. 11.What is 57²? =
  12. 12.How many whole numbers lie between 20² and 21²?
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 352 (b) 324 (c) 328
  15. 15.A square garden has an area of 361 square m. How long is each side (in m)?
  16. 16.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  17. 17.A square garden has an area of 441 square m. How long is each side (in m)?
  18. 18.A square garden has an area of 400 square m. How long is each side (in m)?
  19. 19.Which of these is a perfect square? (a) 1089 (b) 1139 (c) 1110
  20. 20.What is 84²? =
  21. 21.A square garden has an area of 529 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 821 (b) 784 (c) 800
  23. 23.How many whole numbers lie between 10² and 11²?
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 108 must be divided to get a perfect square?
  27. 27.What is the smallest whole number by which 192 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 5² and 6²?
  29. 29.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  30. 30.What is 48²? =
  31. 31.A square garden has an area of 36 square m. How long is each side (in m)?
  32. 32.What is 12²? =
  33. 33.A square garden has an area of 1681 square m. How long is each side (in m)?
  34. 34.What is √1521? =
  35. 35.Which of these is a perfect square? (a) 1305 (b) 1296 (c) 1338
  36. 36.What is the smallest whole number by which 832 must be divided to get a perfect square?
  37. 37.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  38. 38.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 121 square m. How long is each side (in m)?
  40. 40.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 47
  2. 676
  3. 1225
  4. 6
  5. 36
  6. 529
  7. 169
  8. 22
  9. 196
  10. 2
  11. 3249
  12. 40
  13. 900
  14. 324
  15. 19
  16. 100
  17. 21
  18. 20
  19. 1089
  20. 7056
  21. 23
  22. 784
  23. 20
  24. 121
  25. 14
  26. 3
  27. 3
  28. 10
  29. 10
  30. 2304
  31. 6
  32. 144
  33. 41
  34. 39
  35. 1296
  36. 13
  37. 5
  38. 484
  39. 11
  40. 81

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