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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 194 · 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 46² and 47²?
  2. 2.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 460 (b) 480 (c) 441
  4. 4.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 47² and 48²?
  6. 6.A square garden has an area of 961 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 2916 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 751 (b) 729 (c) 746
  9. 9.How many whole numbers lie between 28² and 29²?
  10. 10.What is 32²? =
  11. 11.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 704 must be divided to get a perfect square?
  14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √484? =
  16. 16.What is 15²? =
  17. 17.Which of these is a perfect square? (a) 1096 (b) 1089 (c) 1110
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 42²? =
  20. 20.What is 60²? =
  21. 21.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  23. 23.What is 73²? =
  24. 24.What is 21²? =
  25. 25.Which of these is a perfect square? (a) 900 (b) 938 (c) 934
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  27. 27.Which of these is a perfect square? (a) 1301 (b) 1299 (c) 1296
  28. 28.How many whole numbers lie between 7² and 8²?
  29. 29.What is √3969? =
  30. 30.A square garden has an area of 2500 square m. How long is each side (in m)?
  31. 31.What is 11²? =
  32. 32.What is the smallest whole number by which 320 must be divided to get a perfect square?
  33. 33.How many whole numbers lie between 5² and 6²?
  34. 34.What is 18²? =
  35. 35.How many whole numbers lie between 8² and 9²?
  36. 36.What is √7225? =
  37. 37.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  38. 38.A square garden has an area of 1024 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 275 must be divided to get a perfect square?
  40. 40.A square garden has an area of 100 square m. How long is each side (in m)?

Answer key

  1. 92
  2. 6
  3. 441
  4. 15
  5. 94
  6. 31
  7. 54
  8. 729
  9. 56
  10. 1024
  11. 729
  12. 36
  13. 11
  14. 676
  15. 22
  16. 225
  17. 1089
  18. 289
  19. 1764
  20. 3600
  21. 400
  22. 2
  23. 5329
  24. 441
  25. 900
  26. 100
  27. 1296
  28. 14
  29. 63
  30. 50
  31. 121
  32. 5
  33. 10
  34. 324
  35. 16
  36. 85
  37. 14
  38. 32
  39. 11
  40. 10

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