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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 575 · 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.A square garden has an area of 256 square m. How long is each side (in m)?
  2. 2.A square garden has an area of 3249 square m. How long is each side (in m)?
  3. 3.How many whole numbers lie between 41² and 42²?
  4. 4.Which of these is a perfect square? (a) 307 (b) 291 (c) 289
  5. 5.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  6. 6.A square garden has an area of 1225 square m. How long is each side (in m)?
  7. 7.What is √5625? =
  8. 8.How many whole numbers lie between 30² and 31²?
  9. 9.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  10. 10.What is √4624? =
  11. 11.How many whole numbers lie between 14² and 15²?
  12. 12.What is √529? =
  13. 13.How many whole numbers lie between 24² and 25²?
  14. 14.What is 31²? =
  15. 15.Which of these is a perfect square? (a) 234 (b) 225 (c) 231
  16. 16.How many whole numbers lie between 38² and 39²?
  17. 17.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √729? =
  21. 21.What is the smallest whole number by which 117 must be divided to get a perfect square?
  22. 22.What is 88²? =
  23. 23.What is the smallest whole number by which 176 must be divided to get a perfect square?
  24. 24.Which of these is a perfect square? (a) 1005 (b) 961 (c) 962
  25. 25.Which of these is a perfect square? (a) 394 (b) 379 (c) 361
  26. 26.What is the smallest whole number by which 250 must be divided to get a perfect square?
  27. 27.A square garden has an area of 2704 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 3136 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 1296 square m. How long is each side (in m)?
  31. 31.A square garden has an area of 2116 square m. How long is each side (in m)?
  32. 32.What is 40²? =
  33. 33.How many whole numbers lie between 36² and 37²?
  34. 34.What is √6561? =
  35. 35.What is √3481? =
  36. 36.What is √144? =
  37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  39. 39.What is 38²? =
  40. 40.What is √2704? =

Answer key

  1. 16
  2. 57
  3. 82
  4. 289
  5. 15
  6. 35
  7. 75
  8. 60
  9. 13
  10. 68
  11. 28
  12. 23
  13. 48
  14. 961
  15. 225
  16. 76
  17. 144
  18. 25
  19. 484
  20. 27
  21. 13
  22. 7744
  23. 11
  24. 961
  25. 361
  26. 10
  27. 52
  28. 729
  29. 56
  30. 36
  31. 46
  32. 1600
  33. 72
  34. 81
  35. 59
  36. 12
  37. 400
  38. 2
  39. 1444
  40. 52

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