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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 691 · 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 √6724? =
  2. 2.What is 33²? =
  3. 3.How many whole numbers lie between 40² and 41²?
  4. 4.A square garden has an area of 256 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 983 (b) 961 (c) 997
  6. 6.What is the smallest whole number by which 52 must be divided to get a perfect square?
  7. 7.How many whole numbers lie between 32² and 33²?
  8. 8.A square garden has an area of 729 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 8² and 9²?
  10. 10.A square garden has an area of 3364 square m. How long is each side (in m)?
  11. 11.What is √9216? =
  12. 12.What is 79²? =
  13. 13.A square garden has an area of 2809 square m. How long is each side (in m)?
  14. 14.How many whole numbers lie between 48² and 49²?
  15. 15.How many whole numbers lie between 25² and 26²?
  16. 16.A square garden has an area of 289 square m. How long is each side (in m)?
  17. 17.What is 59²? =
  18. 18.What is √2401? =
  19. 19.What is 48²? =
  20. 20.What is 32²? =
  21. 21.A square garden has an area of 1521 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 686 must be divided to get a perfect square?
  23. 23.What is √529? =
  24. 24.How many whole numbers lie between 27² and 28²?
  25. 25.A square garden has an area of 36 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 1547 (b) 1531 (c) 1521
  27. 27.A square garden has an area of 961 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √1089? =
  30. 30.How many whole numbers lie between 18² and 19²?
  31. 31.Which of these is a perfect square? (a) 324 (b) 341 (c) 355
  32. 32.What is √6241? =
  33. 33.What is the smallest whole number by which 162 must be divided to get a perfect square?
  34. 34.A square garden has an area of 1681 square m. How long is each side (in m)?
  35. 35.What is the smallest whole number by which 252 must be divided to get a perfect square?
  36. 36.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 64 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 169 (b) 192 (c) 187

Answer key

  1. 82
  2. 1089
  3. 80
  4. 16
  5. 961
  6. 13
  7. 64
  8. 27
  9. 16
  10. 58
  11. 96
  12. 6241
  13. 53
  14. 96
  15. 50
  16. 17
  17. 3481
  18. 49
  19. 2304
  20. 1024
  21. 39
  22. 14
  23. 23
  24. 54
  25. 6
  26. 1521
  27. 31
  28. 36
  29. 33
  30. 36
  31. 324
  32. 79
  33. 2
  34. 41
  35. 7
  36. 11
  37. 729
  38. 25
  39. 8
  40. 169

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