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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 424 · 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 √361? =
  2. 2.What is the smallest whole number by which 686 must be divided to get a perfect square?
  3. 3.What is √9216? =
  4. 4.What is √2704? =
  5. 5.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  6. 6.How many whole numbers lie between 13² and 14²?
  7. 7.What is 56²? =
  8. 8.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 50²? =
  10. 10.How many whole numbers lie between 12² and 13²?
  11. 11.How many whole numbers lie between 45² and 46²?
  12. 12.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 28² and 29²?
  14. 14.What is the smallest whole number by which 56 must be divided to get a perfect square?
  15. 15.What is 67²? =
  16. 16.Which of these is a perfect square? (a) 158 (b) 150 (c) 144
  17. 17.Which of these is a perfect square? (a) 625 (b) 657 (c) 636
  18. 18.Which of these is a perfect square? (a) 315 (b) 314 (c) 289
  19. 19.What is √3136? =
  20. 20.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  21. 21.How many whole numbers lie between 17² and 18²?
  22. 22.What is √1681? =
  23. 23.What is 42²? =
  24. 24.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 66²? =
  26. 26.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 2209 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the smallest whole number by which 160 must be divided to get a perfect square?
  30. 30.A square garden has an area of 400 square m. How long is each side (in m)?
  31. 31.What is 73²? =
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is √289? =
  34. 34.What is √121? =
  35. 35.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  36. 36.What is √6889? =
  37. 37.What is √6400? =
  38. 38.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 1450 (b) 1485 (c) 1444
  40. 40.A square garden has an area of 1156 square m. How long is each side (in m)?

Answer key

  1. 19
  2. 14
  3. 96
  4. 52
  5. 3
  6. 26
  7. 3136
  8. 289
  9. 2500
  10. 24
  11. 90
  12. 529
  13. 56
  14. 14
  15. 4489
  16. 144
  17. 625
  18. 289
  19. 56
  20. 3
  21. 34
  22. 41
  23. 1764
  24. 841
  25. 4356
  26. 676
  27. 47
  28. 256
  29. 10
  30. 20
  31. 5329
  32. 324
  33. 17
  34. 11
  35. 7
  36. 83
  37. 80
  38. 14
  39. 1444
  40. 34

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