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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 546 · 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.How many whole numbers lie between 29² and 30²?
  2. 2.What is 48²? =
  3. 3.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √2025? =
  6. 6.How many whole numbers lie between 15² and 16²?
  7. 7.What is the smallest whole number by which 90 must be divided to get a perfect square?
  8. 8.A square garden has an area of 2304 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 36² and 37²?
  10. 10.What is √5625? =
  11. 11.Which of these is a perfect square? (a) 1252 (b) 1238 (c) 1225
  12. 12.What is 92²? =
  13. 13.What is 43²? =
  14. 14.A square garden has an area of 361 square m. How long is each side (in m)?
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  18. 18.What is 83²? =
  19. 19.Which of these is a perfect square? (a) 408 (b) 400 (c) 431
  20. 20.What is 11²? =
  21. 21.Which of these is a perfect square? (a) 676 (b) 700 (c) 679
  22. 22.What is √6561? =
  23. 23.What is 95²? =
  24. 24.How many whole numbers lie between 5² and 6²?
  25. 25.What is 46²? =
  26. 26.What is 52²? =
  27. 27.How many whole numbers lie between 14² and 15²?
  28. 28.What is 93²? =
  29. 29.Which of these is a perfect square? (a) 576 (b) 595 (c) 605
  30. 30.A square garden has an area of 484 square m. How long is each side (in m)?
  31. 31.What is √1521? =
  32. 32.A square garden has an area of 36 square m. How long is each side (in m)?
  33. 33.What is √4624? =
  34. 34.What is 65²? =
  35. 35.What is √1764? =
  36. 36.What is √529? =
  37. 37.What is √256? =
  38. 38.Which of these is a perfect square? (a) 205 (b) 223 (c) 196
  39. 39.How many whole numbers lie between 25² and 26²?
  40. 40.What is the smallest whole number by which 12 must be multiplied to get a perfect square?

Answer key

  1. 58
  2. 2304
  3. 144
  4. 529
  5. 45
  6. 30
  7. 10
  8. 48
  9. 72
  10. 75
  11. 1225
  12. 8464
  13. 1849
  14. 19
  15. 324
  16. 784
  17. 6
  18. 6889
  19. 400
  20. 121
  21. 676
  22. 81
  23. 9025
  24. 10
  25. 2116
  26. 2704
  27. 28
  28. 8649
  29. 576
  30. 22
  31. 39
  32. 6
  33. 68
  34. 4225
  35. 42
  36. 23
  37. 16
  38. 196
  39. 50
  40. 3

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