← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 627 · 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 the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √6241? =
  3. 3.How many whole numbers lie between 15² and 16²?
  4. 4.Which of these is a perfect square? (a) 219 (b) 196 (c) 207
  5. 5.A square garden has an area of 3136 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  7. 7.What is 31²? =
  8. 8.What is √961? =
  9. 9.What is 94²? =
  10. 10.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  11. 11.How many whole numbers lie between 32² and 33²?
  12. 12.What is √3136? =
  13. 13.A square garden has an area of 1156 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 727 (b) 676 (c) 682
  15. 15.A square garden has an area of 1764 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 180 must be divided to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 385 (b) 391 (c) 361
  18. 18.What is 65²? =
  19. 19.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  20. 20.Which of these is a perfect square? (a) 513 (b) 516 (c) 484
  21. 21.What is √289? =
  22. 22.A square garden has an area of 1296 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 35² and 36²?
  24. 24.What is 96²? =
  25. 25.How many whole numbers lie between 20² and 21²?
  26. 26.A square garden has an area of 3600 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 34² and 35²?
  28. 28.What is √8100? =
  29. 29.What is 76²? =
  30. 30.A square garden has an area of 3364 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 1243 (b) 1225 (c) 1229
  33. 33.A square garden has an area of 225 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 1089 (b) 1152 (c) 1144
  35. 35.Which of these is a perfect square? (a) 1507 (b) 1444 (c) 1474
  36. 36.What is 39²? =
  37. 37.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 39² and 40²?
  39. 39.What is 92²? =
  40. 40.How many whole numbers lie between 27² and 28²?

Answer key

  1. 625
  2. 79
  3. 30
  4. 196
  5. 56
  6. 2
  7. 961
  8. 31
  9. 8836
  10. 10
  11. 64
  12. 56
  13. 34
  14. 676
  15. 42
  16. 5
  17. 361
  18. 4225
  19. 256
  20. 484
  21. 17
  22. 36
  23. 70
  24. 9216
  25. 40
  26. 60
  27. 68
  28. 90
  29. 5776
  30. 58
  31. 7
  32. 1225
  33. 15
  34. 1089
  35. 1444
  36. 1521
  37. 225
  38. 78
  39. 8464
  40. 54

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