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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 351 · 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 729 square m. How long is each side (in m)?
  2. 2.A square garden has an area of 1369 square m. How long is each side (in m)?
  3. 3.Which of these is a perfect square? (a) 242 (b) 225 (c) 248
  4. 4.What is √4900? =
  5. 5.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 1042 (b) 1024 (c) 1035
  7. 7.Which of these is a perfect square? (a) 1389 (b) 1369 (c) 1405
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the smallest whole number by which 108 must be divided to get a perfect square?
  10. 10.Which of these is a perfect square? (a) 277 (b) 256 (c) 282
  11. 11.A square garden has an area of 225 square m. How long is each side (in m)?
  12. 12.What is √4761? =
  13. 13.What is 35²? =
  14. 14.What is √7744? =
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  16. 16.How many whole numbers lie between 33² and 34²?
  17. 17.A square garden has an area of 1764 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 15² and 16²?
  19. 19.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  20. 20.How many whole numbers lie between 19² and 20²?
  21. 21.How many whole numbers lie between 16² and 17²?
  22. 22.What is √8836? =
  23. 23.What is 72²? =
  24. 24.What is 18²? =
  25. 25.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 52 must be divided to get a perfect square?
  27. 27.What is the smallest whole number by which 60 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 18² and 19²?
  29. 29.Which of these is a perfect square? (a) 441 (b) 465 (c) 475
  30. 30.A square garden has an area of 1225 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  32. 32.What is the smallest whole number by which 90 must be divided to get a perfect square?
  33. 33.What is √2025? =
  34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 29²? =
  36. 36.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  37. 37.What is √9409? =
  38. 38.Which of these is a perfect square? (a) 1600 (b) 1636 (c) 1680
  39. 39.What is √8464? =
  40. 40.How many whole numbers lie between 43² and 44²?

Answer key

  1. 27
  2. 37
  3. 225
  4. 70
  5. 2
  6. 1024
  7. 1369
  8. 36
  9. 3
  10. 256
  11. 15
  12. 69
  13. 1225
  14. 88
  15. 361
  16. 66
  17. 42
  18. 30
  19. 6
  20. 38
  21. 32
  22. 94
  23. 5184
  24. 324
  25. 3
  26. 13
  27. 15
  28. 36
  29. 441
  30. 35
  31. 6
  32. 10
  33. 45
  34. 625
  35. 841
  36. 6
  37. 97
  38. 1600
  39. 92
  40. 86

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