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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 720 · 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 35² and 36²?
  2. 2.What is 58²? =
  3. 3.A square garden has an area of 144 square m. How long is each side (in m)?
  4. 4.A square garden has an area of 3481 square m. How long is each side (in m)?
  5. 5.What is √8464? =
  6. 6.Which of these is a perfect square? (a) 216 (b) 219 (c) 196
  7. 7.A square garden has an area of 36 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 36² and 37²?
  10. 10.Which of these is a perfect square? (a) 417 (b) 430 (c) 400
  11. 11.Which of these is a perfect square? (a) 262 (b) 256 (c) 264
  12. 12.A square garden has an area of 961 square m. How long is each side (in m)?
  13. 13.What is 95²? =
  14. 14.What is 26²? =
  15. 15.What is √3136? =
  16. 16.Which of these is a perfect square? (a) 1521 (b) 1526 (c) 1535
  17. 17.Which of these is a perfect square? (a) 1087 (b) 1024 (c) 1059
  18. 18.How many whole numbers lie between 33² and 34²?
  19. 19.How many whole numbers lie between 24² and 25²?
  20. 20.What is 21²? =
  21. 21.What is 54²? =
  22. 22.A square garden has an area of 49 square m. How long is each side (in m)?
  23. 23.What is 47²? =
  24. 24.What is 51²? =
  25. 25.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  27. 27.Which of these is a perfect square? (a) 723 (b) 711 (c) 676
  28. 28.How many whole numbers lie between 48² and 49²?
  29. 29.What is √576? =
  30. 30.What is 40²? =
  31. 31.A square garden has an area of 1225 square m. How long is each side (in m)?
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 7² and 8²?
  34. 34.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √900? =
  36. 36.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  37. 37.What is √2704? =
  38. 38.What is 88²? =
  39. 39.Which of these is a perfect square? (a) 338 (b) 324 (c) 352
  40. 40.What is √8100? =

Answer key

  1. 70
  2. 3364
  3. 12
  4. 59
  5. 92
  6. 196
  7. 6
  8. 196
  9. 72
  10. 400
  11. 256
  12. 31
  13. 9025
  14. 676
  15. 56
  16. 1521
  17. 1024
  18. 66
  19. 48
  20. 441
  21. 2916
  22. 7
  23. 2209
  24. 2601
  25. 6
  26. 529
  27. 676
  28. 96
  29. 24
  30. 1600
  31. 35
  32. 324
  33. 14
  34. 64
  35. 30
  36. 2
  37. 52
  38. 7744
  39. 324
  40. 90

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