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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 154 · 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 smallest whole number by which 686 must be divided to get a perfect square?
  2. 2.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 113 (b) 100 (c) 102
  4. 4.What is √3721? =
  5. 5.What is √2304? =
  6. 6.How many whole numbers lie between 7² and 8²?
  7. 7.How many whole numbers lie between 35² and 36²?
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 44²? =
  10. 10.How many whole numbers lie between 39² and 40²?
  11. 11.What is 21²? =
  12. 12.How many whole numbers lie between 41² and 42²?
  13. 13.What is 43²? =
  14. 14.What is the smallest whole number by which 294 must be divided to get a perfect square?
  15. 15.What is the smallest whole number by which 44 must be divided to get a perfect square?
  16. 16.What is √2601? =
  17. 17.A square garden has an area of 36 square m. How long is each side (in m)?
  18. 18.What is √256? =
  19. 19.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  20. 20.What is 23²? =
  21. 21.What is 22²? =
  22. 22.What is the smallest whole number by which 504 must be divided to get a perfect square?
  23. 23.A square garden has an area of 1521 square m. How long is each side (in m)?
  24. 24.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  25. 25.Which of these is a perfect square? (a) 625 (b) 635 (c) 652
  26. 26.A square garden has an area of 2209 square m. How long is each side (in m)?
  27. 27.What is √3969? =
  28. 28.What is 19²? =
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is 47²? =
  31. 31.How many whole numbers lie between 18² and 19²?
  32. 32.Which of these is a perfect square? (a) 973 (b) 961 (c) 1003
  33. 33.A square garden has an area of 529 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 18 must be divided to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 1061 (b) 1024 (c) 1083
  36. 36.What is √8100? =
  37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  38. 38.Which of these is a perfect square? (a) 139 (b) 121 (c) 135
  39. 39.What is 73²? =
  40. 40.Which of these is a perfect square? (a) 182 (b) 172 (c) 169

Answer key

  1. 14
  2. 5
  3. 100
  4. 61
  5. 48
  6. 14
  7. 70
  8. 900
  9. 1936
  10. 78
  11. 441
  12. 82
  13. 1849
  14. 6
  15. 11
  16. 51
  17. 6
  18. 16
  19. 13
  20. 529
  21. 484
  22. 14
  23. 39
  24. 784
  25. 625
  26. 47
  27. 63
  28. 361
  29. 100
  30. 2209
  31. 36
  32. 961
  33. 23
  34. 2
  35. 1024
  36. 90
  37. 169
  38. 121
  39. 5329
  40. 169

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