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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 434 · 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 √1089? =
  2. 2.Which of these is a perfect square? (a) 729 (b) 745 (c) 768
  3. 3.Which of these is a perfect square? (a) 280 (b) 274 (c) 256
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  6. 6.A square garden has an area of 289 square m. How long is each side (in m)?
  7. 7.What is 33²? =
  8. 8.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  9. 9.What is √8464? =
  10. 10.What is the smallest whole number by which 125 must be divided to get a perfect square?
  11. 11.What is √144? =
  12. 12.How many whole numbers lie between 10² and 11²?
  13. 13.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  14. 14.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 350 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  17. 17.How many whole numbers lie between 23² and 24²?
  18. 18.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  19. 19.A square garden has an area of 961 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 50² and 51²?
  21. 21.Which of these is a perfect square? (a) 501 (b) 484 (c) 518
  22. 22.How many whole numbers lie between 30² and 31²?
  23. 23.A square garden has an area of 324 square m. How long is each side (in m)?
  24. 24.How many whole numbers lie between 45² and 46²?
  25. 25.What is 35²? =
  26. 26.How many whole numbers lie between 47² and 48²?
  27. 27.What is the smallest whole number by which 20 must be divided to get a perfect square?
  28. 28.A square garden has an area of 2704 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 28² and 29²?
  30. 30.What is √225? =
  31. 31.What is √2401? =
  32. 32.How many whole numbers lie between 39² and 40²?
  33. 33.A square garden has an area of 676 square m. How long is each side (in m)?
  34. 34.A square garden has an area of 2500 square m. How long is each side (in m)?
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  36. 36.How many whole numbers lie between 46² and 47²?
  37. 37.What is 45²? =
  38. 38.What is the smallest whole number by which 960 must be divided to get a perfect square?
  39. 39.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  40. 40.A square garden has an area of 2809 square m. How long is each side (in m)?

Answer key

  1. 33
  2. 729
  3. 256
  4. 64
  5. 13
  6. 17
  7. 1089
  8. 3
  9. 92
  10. 5
  11. 12
  12. 20
  13. 3
  14. 400
  15. 14
  16. 13
  17. 46
  18. 14
  19. 31
  20. 100
  21. 484
  22. 60
  23. 18
  24. 90
  25. 1225
  26. 94
  27. 5
  28. 52
  29. 56
  30. 15
  31. 49
  32. 78
  33. 26
  34. 50
  35. 121
  36. 92
  37. 2025
  38. 15
  39. 5
  40. 53

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