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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 182 · 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.Which of these is a perfect square? (a) 289 (b) 290 (c) 311
  2. 2.A square garden has an area of 2500 square m. How long is each side (in m)?
  3. 3.Which of these is a perfect square? (a) 560 (b) 547 (c) 529
  4. 4.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  5. 5.What is 34²? =
  6. 6.What is 94²? =
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  8. 8.A square garden has an area of 841 square m. How long is each side (in m)?
  9. 9.What is 76²? =
  10. 10.Which of these is a perfect square? (a) 1563 (b) 1566 (c) 1521
  11. 11.What is √2401? =
  12. 12.Which of these is a perfect square? (a) 961 (b) 1014 (c) 974
  13. 13.How many whole numbers lie between 49² and 50²?
  14. 14.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  15. 15.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  16. 16.A square garden has an area of 256 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  18. 18.How many whole numbers lie between 14² and 15²?
  19. 19.What is 80²? =
  20. 20.What is the smallest whole number by which 208 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 256 (b) 276 (c) 273
  22. 22.A square garden has an area of 961 square m. How long is each side (in m)?
  23. 23.What is 32²? =
  24. 24.A square garden has an area of 2209 square m. How long is each side (in m)?
  25. 25.What is 21²? =
  26. 26.What is 52²? =
  27. 27.What is √2809? =
  28. 28.Which of these is a perfect square? (a) 1600 (b) 1669 (c) 1641
  29. 29.What is the smallest whole number by which 160 must be divided to get a perfect square?
  30. 30.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  31. 31.What is √289? =
  32. 32.What is 83²? =
  33. 33.How many whole numbers lie between 47² and 48²?
  34. 34.What is √625? =
  35. 35.What is √3249? =
  36. 36.How many whole numbers lie between 11² and 12²?
  37. 37.What is 20²? =
  38. 38.What is 29²? =
  39. 39.A square garden has an area of 1156 square m. How long is each side (in m)?
  40. 40.What is 96²? =

Answer key

  1. 289
  2. 50
  3. 529
  4. 15
  5. 1156
  6. 8836
  7. 729
  8. 29
  9. 5776
  10. 1521
  11. 49
  12. 961
  13. 98
  14. 5
  15. 49
  16. 16
  17. 10
  18. 28
  19. 6400
  20. 13
  21. 256
  22. 31
  23. 1024
  24. 47
  25. 441
  26. 2704
  27. 53
  28. 1600
  29. 10
  30. 15
  31. 17
  32. 6889
  33. 94
  34. 25
  35. 57
  36. 22
  37. 400
  38. 841
  39. 34
  40. 9216

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