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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 53 · 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 51²? =
  2. 2.How many whole numbers lie between 6² and 7²?
  3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 36² and 37²?
  5. 5.Which of these is a perfect square? (a) 1024 (b) 1053 (c) 1066
  6. 6.What is √3600? =
  7. 7.A square garden has an area of 400 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the smallest whole number by which 60 must be divided to get a perfect square?
  10. 10.What is the smallest whole number by which 539 must be divided to get a perfect square?
  11. 11.What is 77²? =
  12. 12.How many whole numbers lie between 45² and 46²?
  13. 13.How many whole numbers lie between 47² and 48²?
  14. 14.Which of these is a perfect square? (a) 900 (b) 928 (c) 921
  15. 15.A square garden has an area of 289 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 7² and 8²?
  17. 17.What is √441? =
  18. 18.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 35²? =
  20. 20.How many whole numbers lie between 11² and 12²?
  21. 21.What is 66²? =
  22. 22.What is the smallest whole number by which 325 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 49² and 50²?
  24. 24.What is the smallest whole number by which 384 must be divided to get a perfect square?
  25. 25.What is 90²? =
  26. 26.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  27. 27.What is √6084? =
  28. 28.How many whole numbers lie between 16² and 17²?
  29. 29.What is 21²? =
  30. 30.How many whole numbers lie between 32² and 33²?
  31. 31.What is √225? =
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 10² and 11²?
  34. 34.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  35. 35.A square garden has an area of 144 square m. How long is each side (in m)?
  36. 36.What is √9604? =
  37. 37.A square garden has an area of 81 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 21² and 22²?
  39. 39.What is 73²? =
  40. 40.A square garden has an area of 100 square m. How long is each side (in m)?

Answer key

  1. 2601
  2. 12
  3. 361
  4. 72
  5. 1024
  6. 60
  7. 20
  8. 81
  9. 15
  10. 11
  11. 5929
  12. 90
  13. 94
  14. 900
  15. 17
  16. 14
  17. 21
  18. 49
  19. 1225
  20. 22
  21. 4356
  22. 13
  23. 98
  24. 6
  25. 8100
  26. 6
  27. 78
  28. 32
  29. 441
  30. 64
  31. 15
  32. 256
  33. 20
  34. 2
  35. 12
  36. 98
  37. 9
  38. 42
  39. 5329
  40. 10

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