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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 236 · 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 38² and 39²?
  2. 2.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 448 (b) 441 (c) 444
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 36² and 37²?
  6. 6.How many whole numbers lie between 8² and 9²?
  7. 7.What is √4900? =
  8. 8.How many whole numbers lie between 29² and 30²?
  9. 9.What is √9409? =
  10. 10.What is 48²? =
  11. 11.Which of these is a perfect square? (a) 361 (b) 369 (c) 380
  12. 12.What is √4489? =
  13. 13.What is √7056? =
  14. 14.Which of these is a perfect square? (a) 635 (b) 625 (c) 643
  15. 15.Which of these is a perfect square? (a) 413 (b) 418 (c) 400
  16. 16.What is √625? =
  17. 17.A square garden has an area of 1764 square m. How long is each side (in m)?
  18. 18.What is 17²? =
  19. 19.How many whole numbers lie between 48² and 49²?
  20. 20.Which of these is a perfect square? (a) 841 (b) 848 (c) 865
  21. 21.What is the smallest whole number by which 126 must be divided to get a perfect square?
  22. 22.What is √4624? =
  23. 23.How many whole numbers lie between 45² and 46²?
  24. 24.Which of these is a perfect square? (a) 807 (b) 784 (c) 816
  25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 1369 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 1024 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 196 square m. How long is each side (in m)?
  30. 30.How many whole numbers lie between 5² and 6²?
  31. 31.How many whole numbers lie between 20² and 21²?
  32. 32.What is the smallest whole number by which 18 must be divided to get a perfect square?
  33. 33.What is 54²? =
  34. 34.A square garden has an area of 3600 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 33² and 34²?
  36. 36.How many whole numbers lie between 39² and 40²?
  37. 37.What is 74²? =
  38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 355 (b) 324 (c) 338
  40. 40.Which of these is a perfect square? (a) 169 (b) 179 (c) 171

Answer key

  1. 76
  2. 2
  3. 441
  4. 900
  5. 72
  6. 16
  7. 70
  8. 58
  9. 97
  10. 2304
  11. 361
  12. 67
  13. 84
  14. 625
  15. 400
  16. 25
  17. 42
  18. 289
  19. 96
  20. 841
  21. 14
  22. 68
  23. 90
  24. 784
  25. 25
  26. 37
  27. 36
  28. 32
  29. 14
  30. 10
  31. 40
  32. 2
  33. 2916
  34. 60
  35. 66
  36. 78
  37. 5476
  38. 784
  39. 324
  40. 169

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