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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 203 · 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 162 must be divided to get a perfect square?
  2. 2.How many whole numbers lie between 13² and 14²?
  3. 3.How many whole numbers lie between 47² and 48²?
  4. 4.What is √3249? =
  5. 5.What is the smallest whole number by which 112 must be divided to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 100 (b) 120 (c) 101
  7. 7.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  8. 8.What is √8649? =
  9. 9.What is √2704? =
  10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 170 (b) 169 (c) 183
  12. 12.How many whole numbers lie between 5² and 6²?
  13. 13.Which of these is a perfect square? (a) 330 (b) 347 (c) 324
  14. 14.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  15. 15.How many whole numbers lie between 12² and 13²?
  16. 16.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  17. 17.What is 26²? =
  18. 18.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 55²? =
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  22. 22.Which of these is a perfect square? (a) 482 (b) 460 (c) 441
  23. 23.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  24. 24.What is √169? =
  25. 25.What is √6889? =
  26. 26.A square garden has an area of 3249 square m. How long is each side (in m)?
  27. 27.What is √7396? =
  28. 28.A square garden has an area of 2809 square m. How long is each side (in m)?
  29. 29.What is 47²? =
  30. 30.What is √6241? =
  31. 31.A square garden has an area of 625 square m. How long is each side (in m)?
  32. 32.What is 20²? =
  33. 33.What is the smallest whole number by which 375 must be divided to get a perfect square?
  34. 34.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  35. 35.What is √729? =
  36. 36.Which of these is a perfect square? (a) 828 (b) 784 (c) 790
  37. 37.How many whole numbers lie between 34² and 35²?
  38. 38.What is √676? =
  39. 39.A square garden has an area of 1764 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 169 square m. How long is each side (in m)?

Answer key

  1. 2
  2. 26
  3. 94
  4. 57
  5. 7
  6. 100
  7. 10
  8. 93
  9. 52
  10. 144
  11. 169
  12. 10
  13. 324
  14. 5
  15. 24
  16. 10
  17. 676
  18. 25
  19. 3025
  20. 784
  21. 289
  22. 441
  23. 14
  24. 13
  25. 83
  26. 57
  27. 86
  28. 53
  29. 2209
  30. 79
  31. 25
  32. 400
  33. 15
  34. 11
  35. 27
  36. 784
  37. 68
  38. 26
  39. 42
  40. 13

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