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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 484 · 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 the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  2. 2.A square garden has an area of 256 square m. How long is each side (in m)?
  3. 3.What is √2500? =
  4. 4.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 982 (b) 1021 (c) 961
  6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  8. 8.A square garden has an area of 484 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 16² and 17²?
  10. 10.What is 96²? =
  11. 11.What is 67²? =
  12. 12.How many whole numbers lie between 21² and 22²?
  13. 13.What is √225? =
  14. 14.Which of these is a perfect square? (a) 874 (b) 857 (c) 841
  15. 15.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √729? =
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 27 must be divided to get a perfect square?
  19. 19.How many whole numbers lie between 6² and 7²?
  20. 20.What is √3600? =
  21. 21.How many whole numbers lie between 41² and 42²?
  22. 22.Which of these is a perfect square? (a) 1300 (b) 1296 (c) 1357
  23. 23.How many whole numbers lie between 12² and 13²?
  24. 24.What is the smallest whole number by which 162 must be divided to get a perfect square?
  25. 25.What is 92²? =
  26. 26.How many whole numbers lie between 10² and 11²?
  27. 27.Which of these is a perfect square? (a) 262 (b) 264 (c) 256
  28. 28.What is the smallest whole number by which 128 must be divided to get a perfect square?
  29. 29.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  32. 32.A square garden has an area of 1369 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is √3025? =
  35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  37. 37.Which of these is a perfect square? (a) 1507 (b) 1444 (c) 1508
  38. 38.Which of these is a perfect square? (a) 441 (b) 454 (c) 467
  39. 39.How many whole numbers lie between 49² and 50²?
  40. 40.What is √4624? =

Answer key

  1. 784
  2. 16
  3. 50
  4. 6
  5. 961
  6. 529
  7. 11
  8. 22
  9. 32
  10. 9216
  11. 4489
  12. 42
  13. 15
  14. 841
  15. 144
  16. 27
  17. 225
  18. 3
  19. 12
  20. 60
  21. 82
  22. 1296
  23. 24
  24. 2
  25. 8464
  26. 20
  27. 256
  28. 2
  29. 841
  30. 49
  31. 15
  32. 37
  33. 625
  34. 55
  35. 169
  36. 15
  37. 1444
  38. 441
  39. 98
  40. 68

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