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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 376 · 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 16²? =
  2. 2.A square garden has an area of 3481 square m. How long is each side (in m)?
  3. 3.What is 75²? =
  4. 4.Which of these is a perfect square? (a) 1600 (b) 1624 (c) 1611
  5. 5.What is √1681? =
  6. 6.What is the smallest whole number by which 126 must be divided to get a perfect square?
  7. 7.What is 59²? =
  8. 8.What is √4225? =
  9. 9.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 20²? =
  12. 12.What is √5041? =
  13. 13.A square garden has an area of 324 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 142 (b) 125 (c) 121
  15. 15.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  16. 16.What is 91²? =
  17. 17.How many whole numbers lie between 15² and 16²?
  18. 18.Which of these is a perfect square? (a) 100 (b) 114 (c) 104
  19. 19.What is √3969? =
  20. 20.How many whole numbers lie between 27² and 28²?
  21. 21.How many whole numbers lie between 32² and 33²?
  22. 22.Which of these is a perfect square? (a) 1294 (b) 1237 (c) 1225
  23. 23.A square garden has an area of 196 square m. How long is each side (in m)?
  24. 24.What is 39²? =
  25. 25.A square garden has an area of 1936 square m. How long is each side (in m)?
  26. 26.What is √625? =
  27. 27.How many whole numbers lie between 35² and 36²?
  28. 28.What is √7225? =
  29. 29.A square garden has an area of 900 square m. How long is each side (in m)?
  30. 30.What is √8281? =
  31. 31.What is √1156? =
  32. 32.What is 73²? =
  33. 33.What is 68²? =
  34. 34.What is 35²? =
  35. 35.What is √1764? =
  36. 36.What is 48²? =
  37. 37.What is 80²? =
  38. 38.What is 38²? =
  39. 39.What is 21²? =
  40. 40.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 256
  2. 59
  3. 5625
  4. 1600
  5. 41
  6. 14
  7. 3481
  8. 65
  9. 729
  10. 289
  11. 400
  12. 71
  13. 18
  14. 121
  15. 14
  16. 8281
  17. 30
  18. 100
  19. 63
  20. 54
  21. 64
  22. 1225
  23. 14
  24. 1521
  25. 44
  26. 25
  27. 70
  28. 85
  29. 30
  30. 91
  31. 34
  32. 5329
  33. 4624
  34. 1225
  35. 42
  36. 2304
  37. 6400
  38. 1444
  39. 441
  40. 400

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