← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 196 · 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.Which of these is a perfect square? (a) 361 (b) 364 (c) 390
  2. 2.A square garden has an area of 1849 square m. How long is each side (in m)?
  3. 3.What is 89²? =
  4. 4.How many whole numbers lie between 19² and 20²?
  5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 21² and 22²?
  7. 7.What is 63²? =
  8. 8.How many whole numbers lie between 42² and 43²?
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  10. 10.How many whole numbers lie between 50² and 51²?
  11. 11.What is √144? =
  12. 12.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  13. 13.Which of these is a perfect square? (a) 784 (b) 831 (c) 819
  14. 14.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 1764 square m. How long is each side (in m)?
  16. 16.What is √7056? =
  17. 17.A square garden has an area of 1089 square m. How long is each side (in m)?
  18. 18.What is √2809? =
  19. 19.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 69²? =
  21. 21.What is 22²? =
  22. 22.What is 17²? =
  23. 23.What is √729? =
  24. 24.What is √256? =
  25. 25.How many whole numbers lie between 24² and 25²?
  26. 26.What is √576? =
  27. 27.How many whole numbers lie between 7² and 8²?
  28. 28.What is √6400? =
  29. 29.What is 95²? =
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √9801? =
  32. 32.A square garden has an area of 3600 square m. How long is each side (in m)?
  33. 33.What is √8649? =
  34. 34.What is √2209? =
  35. 35.What is √9604? =
  36. 36.What is 23²? =
  37. 37.What is √6084? =
  38. 38.What is √4096? =
  39. 39.What is √7744? =
  40. 40.Which of these is a perfect square? (a) 1041 (b) 1024 (c) 1063

Answer key

  1. 361
  2. 43
  3. 7921
  4. 38
  5. 169
  6. 42
  7. 3969
  8. 84
  9. 49
  10. 100
  11. 12
  12. 64
  13. 784
  14. 441
  15. 42
  16. 84
  17. 33
  18. 53
  19. 729
  20. 4761
  21. 484
  22. 289
  23. 27
  24. 16
  25. 48
  26. 24
  27. 14
  28. 80
  29. 9025
  30. 225
  31. 99
  32. 60
  33. 93
  34. 47
  35. 98
  36. 529
  37. 78
  38. 64
  39. 88
  40. 1024

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