← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 265 · 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.Which of these is a perfect square? (a) 175 (b) 169 (c) 194
  3. 3.What is 81²? =
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  5. 5.Which of these is a perfect square? (a) 106 (b) 120 (c) 100
  6. 6.How many whole numbers lie between 27² and 28²?
  7. 7.What is 35²? =
  8. 8.Which of these is a perfect square? (a) 462 (b) 454 (c) 441
  9. 9.What is 71²? =
  10. 10.What is √1681? =
  11. 11.A square garden has an area of 121 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 29² and 30²?
  13. 13.Which of these is a perfect square? (a) 518 (b) 484 (c) 490
  14. 14.Which of these is a perfect square? (a) 139 (b) 138 (c) 121
  15. 15.What is the smallest whole number by which 832 must be divided to get a perfect square?
  16. 16.How many whole numbers lie between 42² and 43²?
  17. 17.A square garden has an area of 1764 square m. How long is each side (in m)?
  18. 18.Which of these is a perfect square? (a) 968 (b) 961 (c) 1022
  19. 19.A square garden has an area of 961 square m. How long is each side (in m)?
  20. 20.A square garden has an area of 36 square m. How long is each side (in m)?
  21. 21.What is √784? =
  22. 22.How many whole numbers lie between 26² and 27²?
  23. 23.Which of these is a perfect square? (a) 437 (b) 400 (c) 412
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  25. 25.Which of these is a perfect square? (a) 900 (b) 916 (c) 913
  26. 26.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  27. 27.A square garden has an area of 1296 square m. How long is each side (in m)?
  28. 28.What is √121? =
  29. 29.What is √484? =
  30. 30.What is the smallest whole number by which 60 must be divided to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 1089 (b) 1117 (c) 1142
  32. 32.What is 29²? =
  33. 33.How many whole numbers lie between 18² and 19²?
  34. 34.What is 11²? =
  35. 35.How many whole numbers lie between 17² and 18²?
  36. 36.What is √9216? =
  37. 37.What is the smallest whole number by which 45 must be divided to get a perfect square?
  38. 38.What is 93²? =
  39. 39.What is √729? =
  40. 40.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 70
  2. 169
  3. 6561
  4. 196
  5. 100
  6. 54
  7. 1225
  8. 441
  9. 5041
  10. 41
  11. 11
  12. 58
  13. 484
  14. 121
  15. 13
  16. 84
  17. 42
  18. 961
  19. 31
  20. 6
  21. 28
  22. 52
  23. 400
  24. 256
  25. 900
  26. 15
  27. 36
  28. 11
  29. 22
  30. 15
  31. 1089
  32. 841
  33. 36
  34. 121
  35. 34
  36. 96
  37. 5
  38. 8649
  39. 27
  40. 625

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