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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 171 · 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 112 must be multiplied to get a perfect square?
  2. 2.A square garden has an area of 49 square m. How long is each side (in m)?
  3. 3.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  4. 4.What is the smallest whole number by which 832 must be divided to get a perfect square?
  5. 5.A square garden has an area of 2916 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 48 must be divided to get a perfect square?
  7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 50²? =
  9. 9.How many whole numbers lie between 48² and 49²?
  10. 10.A square garden has an area of 784 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 9² and 10²?
  13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 82²? =
  15. 15.What is √6084? =
  16. 16.What is the smallest whole number by which 405 must be divided to get a perfect square?
  17. 17.What is √1764? =
  18. 18.What is 90²? =
  19. 19.Which of these is a perfect square? (a) 373 (b) 388 (c) 361
  20. 20.What is √324? =
  21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 45 must be divided to get a perfect square?
  23. 23.What is √8464? =
  24. 24.What is √1849? =
  25. 25.What is √900? =
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 1369 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  30. 30.What is 52²? =
  31. 31.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  32. 32.What is √169? =
  33. 33.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  34. 34.A square garden has an area of 64 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 36² and 37²?
  36. 36.A square garden has an area of 3249 square m. How long is each side (in m)?
  37. 37.A square garden has an area of 169 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 676 square m. How long is each side (in m)?
  39. 39.What is √841? =
  40. 40.What is 14²? =

Answer key

  1. 7
  2. 7
  3. 10
  4. 13
  5. 54
  6. 3
  7. 400
  8. 2500
  9. 96
  10. 28
  11. 14
  12. 18
  13. 729
  14. 6724
  15. 78
  16. 5
  17. 42
  18. 8100
  19. 361
  20. 18
  21. 484
  22. 5
  23. 92
  24. 43
  25. 30
  26. 81
  27. 841
  28. 37
  29. 10
  30. 2704
  31. 2
  32. 13
  33. 5
  34. 8
  35. 72
  36. 57
  37. 13
  38. 26
  39. 29
  40. 196

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