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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 286 · 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 5² and 6²?
  2. 2.What is 88²? =
  3. 3.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  4. 4.A square garden has an area of 3025 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 841 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 10² and 11²?
  9. 9.A square garden has an area of 729 square m. How long is each side (in m)?
  10. 10.What is 11²? =
  11. 11.What is √6561? =
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 82²? =
  15. 15.What is √1849? =
  16. 16.How many whole numbers lie between 47² and 48²?
  17. 17.What is the smallest whole number by which 54 must be divided to get a perfect square?
  18. 18.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  19. 19.What is the smallest whole number by which 343 must be divided to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 1296 (b) 1301 (c) 1357
  21. 21.How many whole numbers lie between 32² and 33²?
  22. 22.Which of these is a perfect square? (a) 676 (b) 695 (c) 708
  23. 23.What is 98²? =
  24. 24.A square garden has an area of 225 square m. How long is each side (in m)?
  25. 25.What is √1369? =
  26. 26.A square garden has an area of 1444 square m. How long is each side (in m)?
  27. 27.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  28. 28.How many whole numbers lie between 7² and 8²?
  29. 29.Which of these is a perfect square? (a) 297 (b) 289 (c) 290
  30. 30.How many whole numbers lie between 20² and 21²?
  31. 31.What is √529? =
  32. 32.A square garden has an area of 2209 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.A square garden has an area of 196 square m. How long is each side (in m)?
  35. 35.What is √1936? =
  36. 36.What is √1600? =
  37. 37.What is √361? =
  38. 38.How many whole numbers lie between 9² and 10²?
  39. 39.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  40. 40.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 10
  2. 7744
  3. 6
  4. 55
  5. 29
  6. 3
  7. 729
  8. 20
  9. 27
  10. 121
  11. 81
  12. 841
  13. 676
  14. 6724
  15. 43
  16. 94
  17. 6
  18. 10
  19. 7
  20. 1296
  21. 64
  22. 676
  23. 9604
  24. 15
  25. 37
  26. 38
  27. 7
  28. 14
  29. 289
  30. 40
  31. 23
  32. 47
  33. 625
  34. 14
  35. 44
  36. 40
  37. 19
  38. 18
  39. 3
  40. 25

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