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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 204 · 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.Which of these is a perfect square? (a) 345 (b) 324 (c) 325
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √225? =
  4. 4.How many whole numbers lie between 25² and 26²?
  5. 5.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 441 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 625 (b) 634 (c) 647
  13. 13.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is 95²? =
  16. 16.What is 27²? =
  17. 17.What is √8281? =
  18. 18.How many whole numbers lie between 48² and 49²?
  19. 19.What is 24²? =
  20. 20.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  21. 21.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  22. 22.What is √676? =
  23. 23.Which of these is a perfect square? (a) 759 (b) 729 (c) 766
  24. 24.What is √4900? =
  25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 77²? =
  27. 27.What is the smallest whole number by which 60 must be divided to get a perfect square?
  28. 28.What is 56²? =
  29. 29.A square garden has an area of 1444 square m. How long is each side (in m)?
  30. 30.What is 48²? =
  31. 31.What is √3969? =
  32. 32.What is √441? =
  33. 33.What is √6724? =
  34. 34.What is √2025? =
  35. 35.A square garden has an area of 36 square m. How long is each side (in m)?
  36. 36.What is √6241? =
  37. 37.Which of these is a perfect square? (a) 886 (b) 841 (c) 855
  38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 144 (b) 150 (c) 153
  40. 40.What is 30²? =

Answer key

  1. 324
  2. 81
  3. 15
  4. 50
  5. 13
  6. 400
  7. 169
  8. 100
  9. 36
  10. 21
  11. 256
  12. 625
  13. 441
  14. 225
  15. 9025
  16. 729
  17. 91
  18. 96
  19. 576
  20. 5
  21. 11
  22. 26
  23. 729
  24. 70
  25. 484
  26. 5929
  27. 15
  28. 3136
  29. 38
  30. 2304
  31. 63
  32. 21
  33. 82
  34. 45
  35. 6
  36. 79
  37. 841
  38. 289
  39. 144
  40. 900

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