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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 252 · 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 √5476? =
  2. 2.What is √9216? =
  3. 3.Which of these is a perfect square? (a) 676 (b) 696 (c) 721
  4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 7² and 8²?
  6. 6.How many whole numbers lie between 39² and 40²?
  7. 7.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 49 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 196 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 99 must be divided to get a perfect square?
  14. 14.What is the smallest whole number by which 175 must be divided to get a perfect square?
  15. 15.What is √5184? =
  16. 16.A square garden has an area of 529 square m. How long is each side (in m)?
  17. 17.What is √324? =
  18. 18.A square garden has an area of 2704 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 448 must be divided to get a perfect square?
  20. 20.How many whole numbers lie between 38² and 39²?
  21. 21.What is 52²? =
  22. 22.How many whole numbers lie between 23² and 24²?
  23. 23.How many whole numbers lie between 8² and 9²?
  24. 24.What is the smallest whole number by which 637 must be divided to get a perfect square?
  25. 25.What is 41²? =
  26. 26.What is the smallest whole number by which 48 must be divided to get a perfect square?
  27. 27.A square garden has an area of 729 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 192 must be divided to get a perfect square?
  29. 29.What is √169? =
  30. 30.Which of these is a perfect square? (a) 1289 (b) 1229 (c) 1225
  31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √2401? =
  33. 33.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  34. 34.What is 27²? =
  35. 35.What is the smallest whole number by which 735 must be divided to get a perfect square?
  36. 36.How many whole numbers lie between 41² and 42²?
  37. 37.Which of these is a perfect square? (a) 442 (b) 470 (c) 441
  38. 38.What is √4900? =
  39. 39.What is √900? =
  40. 40.What is √6889? =

Answer key

  1. 74
  2. 96
  3. 676
  4. 81
  5. 14
  6. 78
  7. 196
  8. 900
  9. 7
  10. 7
  11. 256
  12. 14
  13. 11
  14. 7
  15. 72
  16. 23
  17. 18
  18. 52
  19. 7
  20. 76
  21. 2704
  22. 46
  23. 16
  24. 13
  25. 1681
  26. 3
  27. 27
  28. 3
  29. 13
  30. 1225
  31. 784
  32. 49
  33. 2
  34. 729
  35. 15
  36. 82
  37. 441
  38. 70
  39. 30
  40. 83

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