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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 73 · 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 √676? =
  2. 2.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  3. 3.How many whole numbers lie between 28² and 29²?
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √289? =
  7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √1156? =
  9. 9.How many whole numbers lie between 22² and 23²?
  10. 10.What is 61²? =
  11. 11.How many whole numbers lie between 12² and 13²?
  12. 12.How many whole numbers lie between 15² and 16²?
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 56²? =
  15. 15.What is 83²? =
  16. 16.What is √7056? =
  17. 17.What is √1296? =
  18. 18.What is √8100? =
  19. 19.What is √7225? =
  20. 20.Which of these is a perfect square? (a) 280 (b) 256 (c) 259
  21. 21.A square garden has an area of 900 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 1444 (b) 1466 (c) 1506
  24. 24.A square garden has an area of 1849 square m. How long is each side (in m)?
  25. 25.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 16²? =
  27. 27.What is √2025? =
  28. 28.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  29. 29.What is √484? =
  30. 30.A square garden has an area of 2809 square m. How long is each side (in m)?
  31. 31.What is 36²? =
  32. 32.What is √6561? =
  33. 33.What is √441? =
  34. 34.How many whole numbers lie between 14² and 15²?
  35. 35.What is 45²? =
  36. 36.What is 78²? =
  37. 37.How many whole numbers lie between 49² and 50²?
  38. 38.What is √1936? =
  39. 39.What is √729? =
  40. 40.What is the smallest whole number by which 126 must be divided to get a perfect square?

Answer key

  1. 26
  2. 6
  3. 56
  4. 121
  5. 529
  6. 17
  7. 900
  8. 34
  9. 44
  10. 3721
  11. 24
  12. 30
  13. 25
  14. 3136
  15. 6889
  16. 84
  17. 36
  18. 90
  19. 85
  20. 256
  21. 30
  22. 3
  23. 1444
  24. 43
  25. 64
  26. 256
  27. 45
  28. 5
  29. 22
  30. 53
  31. 1296
  32. 81
  33. 21
  34. 28
  35. 2025
  36. 6084
  37. 98
  38. 44
  39. 27
  40. 14

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