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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 470 · 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 the smallest whole number by which 325 must be divided to get a perfect square?
  2. 2.How many whole numbers lie between 19² and 20²?
  3. 3.What is 94²? =
  4. 4.Which of these is a perfect square? (a) 277 (b) 256 (c) 261
  5. 5.What is √1681? =
  6. 6.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  7. 7.What is √4624? =
  8. 8.Which of these is a perfect square? (a) 530 (b) 529 (c) 557
  9. 9.A square garden has an area of 2809 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 523 (b) 484 (c) 514
  11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √6561? =
  13. 13.A square garden has an area of 841 square m. How long is each side (in m)?
  14. 14.How many whole numbers lie between 16² and 17²?
  15. 15.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  16. 16.A square garden has an area of 324 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 48² and 49²?
  18. 18.A square garden has an area of 2116 square m. How long is each side (in m)?
  19. 19.What is √4356? =
  20. 20.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 1225 square m. How long is each side (in m)?
  22. 22.How many whole numbers lie between 5² and 6²?
  23. 23.A square garden has an area of 1024 square m. How long is each side (in m)?
  24. 24.A square garden has an area of 2209 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 3136 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 56 must be divided to get a perfect square?
  27. 27.A square garden has an area of 1521 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 52 must be divided to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 100 (b) 116 (c) 112
  30. 30.A square garden has an area of 961 square m. How long is each side (in m)?
  31. 31.How many whole numbers lie between 40² and 41²?
  32. 32.A square garden has an area of 144 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 10² and 11²?
  34. 34.What is √8464? =
  35. 35.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  36. 36.What is √225? =
  37. 37.Which of these is a perfect square? (a) 841 (b) 871 (c) 848
  38. 38.What is 16²? =
  39. 39.What is √1156? =
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 13
  2. 38
  3. 8836
  4. 256
  5. 41
  6. 13
  7. 68
  8. 529
  9. 53
  10. 484
  11. 361
  12. 81
  13. 29
  14. 32
  15. 3
  16. 18
  17. 96
  18. 46
  19. 66
  20. 5
  21. 35
  22. 10
  23. 32
  24. 47
  25. 56
  26. 14
  27. 39
  28. 13
  29. 100
  30. 31
  31. 80
  32. 12
  33. 20
  34. 92
  35. 7
  36. 15
  37. 841
  38. 256
  39. 34
  40. 36

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