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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 578 · 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 1024 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 1089 (b) 1091 (c) 1119
  3. 3.A square garden has an area of 529 square m. How long is each side (in m)?
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the smallest whole number by which 176 must be divided to get a perfect square?
  6. 6.A square garden has an area of 961 square m. How long is each side (in m)?
  7. 7.What is √6724? =
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √361? =
  10. 10.What is √1369? =
  11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √676? =
  13. 13.What is √4761? =
  14. 14.A square garden has an area of 1444 square m. How long is each side (in m)?
  15. 15.What is √841? =
  16. 16.A square garden has an area of 3025 square m. How long is each side (in m)?
  17. 17.What is √1521? =
  18. 18.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  19. 19.A square garden has an area of 1369 square m. How long is each side (in m)?
  20. 20.What is 32²? =
  21. 21.What is √3600? =
  22. 22.A square garden has an area of 64 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 324 square m. How long is each side (in m)?
  24. 24.What is √289? =
  25. 25.Which of these is a perfect square? (a) 1041 (b) 1024 (c) 1035
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  27. 27.Which of these is a perfect square? (a) 905 (b) 917 (c) 900
  28. 28.A square garden has an area of 2209 square m. How long is each side (in m)?
  29. 29.Which of these is a perfect square? (a) 562 (b) 529 (c) 539
  30. 30.Which of these is a perfect square? (a) 961 (b) 997 (c) 974
  31. 31.Which of these is a perfect square? (a) 228 (b) 253 (c) 225
  32. 32.How many whole numbers lie between 37² and 38²?
  33. 33.What is √8836? =
  34. 34.What is 20²? =
  35. 35.What is 97²? =
  36. 36.Which of these is a perfect square? (a) 676 (b) 714 (c) 695
  37. 37.Which of these is a perfect square? (a) 576 (b) 585 (c) 605
  38. 38.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  39. 39.What is the smallest whole number by which 567 must be divided to get a perfect square?
  40. 40.What is √4096? =

Answer key

  1. 32
  2. 1089
  3. 23
  4. 196
  5. 11
  6. 31
  7. 82
  8. 144
  9. 19
  10. 37
  11. 121
  12. 26
  13. 69
  14. 38
  15. 29
  16. 55
  17. 39
  18. 6
  19. 37
  20. 1024
  21. 60
  22. 8
  23. 18
  24. 17
  25. 1024
  26. 64
  27. 900
  28. 47
  29. 529
  30. 961
  31. 225
  32. 74
  33. 94
  34. 400
  35. 9409
  36. 676
  37. 576
  38. 5
  39. 7
  40. 64

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