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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 422 · 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 29²? =
  2. 2.What is 37²? =
  3. 3.What is √4624? =
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is 50²? =
  6. 6.What is 23²? =
  7. 7.Which of these is a perfect square? (a) 1454 (b) 1485 (c) 1444
  8. 8.Which of these is a perfect square? (a) 216 (b) 220 (c) 196
  9. 9.What is √8836? =
  10. 10.What is 84²? =
  11. 11.What is 55²? =
  12. 12.What is √5625? =
  13. 13.What is 28²? =
  14. 14.How many whole numbers lie between 23² and 24²?
  15. 15.How many whole numbers lie between 25² and 26²?
  16. 16.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  17. 17.What is √361? =
  18. 18.What is √1681? =
  19. 19.What is 24²? =
  20. 20.Which of these is a perfect square? (a) 1665 (b) 1600 (c) 1673
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √1296? =
  24. 24.A square garden has an area of 1296 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √3969? =
  28. 28.How many whole numbers lie between 13² and 14²?
  29. 29.What is 93²? =
  30. 30.How many whole numbers lie between 48² and 49²?
  31. 31.What is 21²? =
  32. 32.A square garden has an area of 25 square m. How long is each side (in m)?
  33. 33.What is √5929? =
  34. 34.What is √2704? =
  35. 35.What is √1849? =
  36. 36.How many whole numbers lie between 11² and 12²?
  37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 41²? =
  40. 40.A square garden has an area of 1681 square m. How long is each side (in m)?

Answer key

  1. 841
  2. 1369
  3. 68
  4. 100
  5. 2500
  6. 529
  7. 1444
  8. 196
  9. 94
  10. 7056
  11. 3025
  12. 75
  13. 784
  14. 46
  15. 50
  16. 2
  17. 19
  18. 41
  19. 576
  20. 1600
  21. 64
  22. 256
  23. 36
  24. 36
  25. 14
  26. 841
  27. 63
  28. 26
  29. 8649
  30. 96
  31. 441
  32. 5
  33. 77
  34. 52
  35. 43
  36. 22
  37. 25
  38. 625
  39. 1681
  40. 41

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