← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 692 · 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 √225? =
  2. 2.Which of these is a perfect square? (a) 359 (b) 331 (c) 324
  3. 3.What is 57²? =
  4. 4.What is 50²? =
  5. 5.What is 42²? =
  6. 6.What is the smallest whole number by which 160 must be divided to get a perfect square?
  7. 7.A square garden has an area of 3600 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 1035 (b) 1037 (c) 1024
  9. 9.Which of these is a perfect square? (a) 1211 (b) 1196 (c) 1156
  10. 10.What is √3025? =
  11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √5041? =
  13. 13.How many whole numbers lie between 29² and 30²?
  14. 14.What is 49²? =
  15. 15.A square garden has an area of 100 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 28² and 29²?
  17. 17.What is √5184? =
  18. 18.How many whole numbers lie between 45² and 46²?
  19. 19.A square garden has an area of 64 square m. How long is each side (in m)?
  20. 20.What is √576? =
  21. 21.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √900? =
  23. 23.What is 40²? =
  24. 24.What is the smallest whole number by which 27 must be divided to get a perfect square?
  25. 25.How many whole numbers lie between 40² and 41²?
  26. 26.How many whole numbers lie between 44² and 45²?
  27. 27.Which of these is a perfect square? (a) 289 (b) 320 (c) 298
  28. 28.What is √3249? =
  29. 29.What is 25²? =
  30. 30.What is 80²? =
  31. 31.A square garden has an area of 484 square m. How long is each side (in m)?
  32. 32.What is 35²? =
  33. 33.Which of these is a perfect square? (a) 1133 (b) 1135 (c) 1089
  34. 34.What is 23²? =
  35. 35.How many whole numbers lie between 10² and 11²?
  36. 36.What is √3844? =
  37. 37.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  38. 38.How many whole numbers lie between 49² and 50²?
  39. 39.What is the smallest whole number by which 810 must be divided to get a perfect square?
  40. 40.What is the smallest whole number by which 108 must be divided to get a perfect square?

Answer key

  1. 15
  2. 324
  3. 3249
  4. 2500
  5. 1764
  6. 10
  7. 60
  8. 1024
  9. 1156
  10. 55
  11. 196
  12. 71
  13. 58
  14. 2401
  15. 10
  16. 56
  17. 72
  18. 90
  19. 8
  20. 24
  21. 225
  22. 30
  23. 1600
  24. 3
  25. 80
  26. 88
  27. 289
  28. 57
  29. 625
  30. 6400
  31. 22
  32. 1225
  33. 1089
  34. 529
  35. 20
  36. 62
  37. 5
  38. 98
  39. 10
  40. 3

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets