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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 524 · 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 the smallest whole number by which 735 must be multiplied to get a perfect square?
  2. 2.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  3. 3.What is √9801? =
  4. 4.What is √576? =
  5. 5.A square garden has an area of 100 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 523 (b) 484 (c) 506
  7. 7.A square garden has an area of 961 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 275 (b) 273 (c) 256
  9. 9.A square garden has an area of 289 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 441 (b) 483 (c) 459
  11. 11.What is √1681? =
  12. 12.Which of these is a perfect square? (a) 676 (b) 697 (c) 698
  13. 13.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  14. 14.What is 85²? =
  15. 15.What is √6400? =
  16. 16.Which of these is a perfect square? (a) 103 (b) 100 (c) 111
  17. 17.A square garden has an area of 841 square m. How long is each side (in m)?
  18. 18.A square garden has an area of 361 square m. How long is each side (in m)?
  19. 19.A square garden has an area of 3600 square m. How long is each side (in m)?
  20. 20.What is 52²? =
  21. 21.What is 32²? =
  22. 22.How many whole numbers lie between 46² and 47²?
  23. 23.How many whole numbers lie between 13² and 14²?
  24. 24.How many whole numbers lie between 25² and 26²?
  25. 25.How many whole numbers lie between 20² and 21²?
  26. 26.A square garden has an area of 1225 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 2025 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 121 square m. How long is each side (in m)?
  29. 29.What is 76²? =
  30. 30.Which of these is a perfect square? (a) 1381 (b) 1378 (c) 1369
  31. 31.A square garden has an area of 625 square m. How long is each side (in m)?
  32. 32.What is 58²? =
  33. 33.What is √8281? =
  34. 34.How many whole numbers lie between 24² and 25²?
  35. 35.What is the smallest whole number by which 486 must be divided to get a perfect square?
  36. 36.What is √2116? =
  37. 37.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  38. 38.Which of these is a perfect square? (a) 144 (b) 163 (c) 167
  39. 39.What is 16²? =
  40. 40.What is 68²? =

Answer key

  1. 15
  2. 6
  3. 99
  4. 24
  5. 10
  6. 484
  7. 31
  8. 256
  9. 17
  10. 441
  11. 41
  12. 676
  13. 11
  14. 7225
  15. 80
  16. 100
  17. 29
  18. 19
  19. 60
  20. 2704
  21. 1024
  22. 92
  23. 26
  24. 50
  25. 40
  26. 35
  27. 45
  28. 11
  29. 5776
  30. 1369
  31. 25
  32. 3364
  33. 91
  34. 48
  35. 6
  36. 46
  37. 13
  38. 144
  39. 256
  40. 4624

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