← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 564 · 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 40² and 41²?
  2. 2.What is √4489? =
  3. 3.What is 41²? =
  4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 17² and 18²?
  6. 6.What is 42²? =
  7. 7.What is the smallest whole number by which 80 must be divided to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 1090 (b) 1094 (c) 1089
  9. 9.Which of these is a perfect square? (a) 829 (b) 784 (c) 832
  10. 10.Which of these is a perfect square? (a) 1552 (b) 1594 (c) 1521
  11. 11.What is √169? =
  12. 12.What is 97²? =
  13. 13.How many whole numbers lie between 15² and 16²?
  14. 14.Which of these is a perfect square? (a) 431 (b) 427 (c) 400
  15. 15.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  16. 16.A square garden has an area of 1156 square m. How long is each side (in m)?
  17. 17.What is 73²? =
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  19. 19.A square garden has an area of 1225 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 1225 (b) 1252 (c) 1234
  21. 21.What is the smallest whole number by which 75 must be divided to get a perfect square?
  22. 22.What is √2809? =
  23. 23.What is √4624? =
  24. 24.What is √225? =
  25. 25.What is the smallest whole number by which 112 must be divided to get a perfect square?
  26. 26.What is 11²? =
  27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √2025? =
  29. 29.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 5² and 6²?
  31. 31.How many whole numbers lie between 24² and 25²?
  32. 32.A square garden has an area of 2916 square m. How long is each side (in m)?
  33. 33.What is 67²? =
  34. 34.What is the smallest whole number by which 72 must be divided to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 729 (b) 775 (c) 748
  36. 36.How many whole numbers lie between 46² and 47²?
  37. 37.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  38. 38.A square garden has an area of 1369 square m. How long is each side (in m)?
  39. 39.What is √5625? =
  40. 40.What is 76²? =

Answer key

  1. 80
  2. 67
  3. 1681
  4. 144
  5. 34
  6. 1764
  7. 5
  8. 1089
  9. 784
  10. 1521
  11. 13
  12. 9409
  13. 30
  14. 400
  15. 25
  16. 34
  17. 5329
  18. 676
  19. 35
  20. 1225
  21. 3
  22. 53
  23. 68
  24. 15
  25. 7
  26. 121
  27. 529
  28. 45
  29. 841
  30. 10
  31. 48
  32. 54
  33. 4489
  34. 2
  35. 729
  36. 92
  37. 5
  38. 37
  39. 75
  40. 5776

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