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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 416 · 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 √7744? =
  2. 2.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 533 (b) 538 (c) 529
  4. 4.What is the smallest whole number by which 27 must be divided to get a perfect square?
  5. 5.What is 94²? =
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 32² and 33²?
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  10. 10.What is 55²? =
  11. 11.How many whole numbers lie between 22² and 23²?
  12. 12.A square garden has an area of 25 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 49² and 50²?
  15. 15.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  17. 17.Which of these is a perfect square? (a) 209 (b) 214 (c) 196
  18. 18.What is √5776? =
  19. 19.How many whole numbers lie between 28² and 29²?
  20. 20.What is √3025? =
  21. 21.How many whole numbers lie between 25² and 26²?
  22. 22.A square garden has an area of 2401 square m. How long is each side (in m)?
  23. 23.What is 58²? =
  24. 24.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  25. 25.What is 68²? =
  26. 26.How many whole numbers lie between 43² and 44²?
  27. 27.How many whole numbers lie between 47² and 48²?
  28. 28.How many whole numbers lie between 39² and 40²?
  29. 29.A square garden has an area of 3136 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is 12²? =
  32. 32.What is √6889? =
  33. 33.What is √625? =
  34. 34.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  35. 35.What is 36²? =
  36. 36.How many whole numbers lie between 27² and 28²?
  37. 37.What is √6561? =
  38. 38.Which of these is a perfect square? (a) 412 (b) 400 (c) 403
  39. 39.Which of these is a perfect square? (a) 149 (b) 144 (c) 162
  40. 40.What is 15²? =

Answer key

  1. 88
  2. 5
  3. 529
  4. 3
  5. 8836
  6. 100
  7. 64
  8. 784
  9. 2
  10. 3025
  11. 44
  12. 5
  13. 529
  14. 98
  15. 11
  16. 36
  17. 196
  18. 76
  19. 56
  20. 55
  21. 50
  22. 49
  23. 3364
  24. 6
  25. 4624
  26. 86
  27. 94
  28. 78
  29. 56
  30. 289
  31. 144
  32. 83
  33. 25
  34. 5
  35. 1296
  36. 54
  37. 81
  38. 400
  39. 144
  40. 225

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