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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 145 · 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 1600 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is 11²? =
  4. 4.What is the smallest whole number by which 12 must be divided to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 324 (b) 341 (c) 337
  6. 6.Which of these is a perfect square? (a) 972 (b) 984 (c) 961
  7. 7.What is √1444? =
  8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 39²? =
  10. 10.Which of these is a perfect square? (a) 169 (b) 171 (c) 181
  11. 11.What is √196? =
  12. 12.What is √5476? =
  13. 13.What is √5041? =
  14. 14.A square garden has an area of 256 square m. How long is each side (in m)?
  15. 15.What is √400? =
  16. 16.What is 85²? =
  17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  18. 18.A square garden has an area of 1024 square m. How long is each side (in m)?
  19. 19.What is √1225? =
  20. 20.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 289 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 135 must be divided to get a perfect square?
  23. 23.What is 36²? =
  24. 24.How many whole numbers lie between 8² and 9²?
  25. 25.What is the smallest whole number by which 640 must be divided to get a perfect square?
  26. 26.How many whole numbers lie between 47² and 48²?
  27. 27.A square garden has an area of 121 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  29. 29.How many whole numbers lie between 33² and 34²?
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  32. 32.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  33. 33.What is √2704? =
  34. 34.How many whole numbers lie between 15² and 16²?
  35. 35.How many whole numbers lie between 18² and 19²?
  36. 36.Which of these is a perfect square? (a) 282 (b) 256 (c) 277
  37. 37.Which of these is a perfect square? (a) 1060 (b) 1038 (c) 1024
  38. 38.What is √5329? =
  39. 39.Which of these is a perfect square? (a) 529 (b) 535 (c) 534
  40. 40.What is 86²? =

Answer key

  1. 40
  2. 729
  3. 121
  4. 3
  5. 324
  6. 961
  7. 38
  8. 361
  9. 1521
  10. 169
  11. 14
  12. 74
  13. 71
  14. 16
  15. 20
  16. 7225
  17. 25
  18. 32
  19. 35
  20. 14
  21. 17
  22. 15
  23. 1296
  24. 16
  25. 10
  26. 94
  27. 11
  28. 81
  29. 66
  30. 324
  31. 10
  32. 6
  33. 52
  34. 30
  35. 36
  36. 256
  37. 1024
  38. 73
  39. 529
  40. 7396

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