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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 547 · 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.A square garden has an area of 1600 square m. How long is each side (in m)?
  2. 2.What is √1296? =
  3. 3.How many whole numbers lie between 44² and 45²?
  4. 4.What is 41²? =
  5. 5.Which of these is a perfect square? (a) 400 (b) 425 (c) 423
  6. 6.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 5² and 6²?
  8. 8.What is √4096? =
  9. 9.What is 23²? =
  10. 10.Which of these is a perfect square? (a) 1296 (b) 1352 (c) 1316
  11. 11.Which of these is a perfect square? (a) 257 (b) 263 (c) 256
  12. 12.A square garden has an area of 3364 square m. How long is each side (in m)?
  13. 13.What is 44²? =
  14. 14.What is the smallest whole number by which 147 must be divided to get a perfect square?
  15. 15.What is √1444? =
  16. 16.What is the smallest whole number by which 405 must be divided to get a perfect square?
  17. 17.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  18. 18.What is √2809? =
  19. 19.What is √3136? =
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 590 (b) 592 (c) 576
  22. 22.How many whole numbers lie between 11² and 12²?
  23. 23.What is 55²? =
  24. 24.What is 33²? =
  25. 25.What is the smallest whole number by which 90 must be divided to get a perfect square?
  26. 26.How many whole numbers lie between 35² and 36²?
  27. 27.What is 60²? =
  28. 28.How many whole numbers lie between 7² and 8²?
  29. 29.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √1369? =
  31. 31.How many whole numbers lie between 26² and 27²?
  32. 32.What is the smallest whole number by which 396 must be divided to get a perfect square?
  33. 33.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  35. 35.How many whole numbers lie between 48² and 49²?
  36. 36.What is 43²? =
  37. 37.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  38. 38.What is 22²? =
  39. 39.What is √8464? =
  40. 40.What is the smallest whole number by which 27 must be multiplied to get a perfect square?

Answer key

  1. 40
  2. 36
  3. 88
  4. 1681
  5. 400
  6. 625
  7. 10
  8. 64
  9. 529
  10. 1296
  11. 256
  12. 58
  13. 1936
  14. 3
  15. 38
  16. 5
  17. 7
  18. 53
  19. 56
  20. 576
  21. 576
  22. 22
  23. 3025
  24. 1089
  25. 10
  26. 70
  27. 3600
  28. 14
  29. 25
  30. 37
  31. 52
  32. 11
  33. 36
  34. 256
  35. 96
  36. 1849
  37. 14
  38. 484
  39. 92
  40. 3

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