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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 301 · 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) 213 (b) 196 (c) 211
  2. 2.What is the smallest whole number by which 135 must be divided to get a perfect square?
  3. 3.What is 35²? =
  4. 4.A square garden has an area of 3136 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 567 must be divided to get a perfect square?
  6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 761 (b) 737 (c) 729
  8. 8.How many whole numbers lie between 23² and 24²?
  9. 9.What is √225? =
  10. 10.A square garden has an area of 2601 square m. How long is each side (in m)?
  11. 11.Which of these is a perfect square? (a) 826 (b) 810 (c) 784
  12. 12.What is √196? =
  13. 13.How many whole numbers lie between 9² and 10²?
  14. 14.A square garden has an area of 25 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 1936 square m. How long is each side (in m)?
  16. 16.Which of these is a perfect square? (a) 254 (b) 225 (c) 228
  17. 17.What is √729? =
  18. 18.What is √6889? =
  19. 19.A square garden has an area of 2809 square m. How long is each side (in m)?
  20. 20.What is 15²? =
  21. 21.Which of these is a perfect square? (a) 1521 (b) 1542 (c) 1586
  22. 22.A square garden has an area of 64 square m. How long is each side (in m)?
  23. 23.What is 60²? =
  24. 24.Which of these is a perfect square? (a) 641 (b) 660 (c) 625
  25. 25.What is the smallest whole number by which 832 must be divided to get a perfect square?
  26. 26.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  27. 27.What is 42²? =
  28. 28.What is √576? =
  29. 29.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 49² and 50²?
  31. 31.What is 28²? =
  32. 32.How many whole numbers lie between 7² and 8²?
  33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is √289? =
  35. 35.How many whole numbers lie between 26² and 27²?
  36. 36.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 18² and 19²?
  39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 45 must be multiplied to get a perfect square?

Answer key

  1. 196
  2. 15
  3. 1225
  4. 56
  5. 7
  6. 144
  7. 729
  8. 46
  9. 15
  10. 51
  11. 784
  12. 14
  13. 18
  14. 5
  15. 44
  16. 225
  17. 27
  18. 83
  19. 53
  20. 225
  21. 1521
  22. 8
  23. 3600
  24. 625
  25. 13
  26. 7
  27. 1764
  28. 24
  29. 289
  30. 98
  31. 784
  32. 14
  33. 400
  34. 17
  35. 52
  36. 6
  37. 529
  38. 36
  39. 484
  40. 5

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