← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 267 · 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 √5625? =
  2. 2.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  3. 3.A square garden has an area of 1369 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √9409? =
  7. 7.A square garden has an area of 2916 square m. How long is each side (in m)?
  8. 8.A square garden has an area of 64 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 17² and 18²?
  10. 10.What is the smallest whole number by which 98 must be divided to get a perfect square?
  11. 11.A square garden has an area of 3025 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 5² and 6²?
  13. 13.How many whole numbers lie between 27² and 28²?
  14. 14.What is 21²? =
  15. 15.Which of these is a perfect square? (a) 1661 (b) 1600 (c) 1679
  16. 16.A square garden has an area of 1681 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  18. 18.A square garden has an area of 3136 square m. How long is each side (in m)?
  19. 19.How many whole numbers lie between 38² and 39²?
  20. 20.Which of these is a perfect square? (a) 711 (b) 685 (c) 676
  21. 21.What is 62²? =
  22. 22.What is √2704? =
  23. 23.How many whole numbers lie between 24² and 25²?
  24. 24.What is √8836? =
  25. 25.How many whole numbers lie between 43² and 44²?
  26. 26.A square garden has an area of 1024 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 7² and 8²?
  28. 28.What is 98²? =
  29. 29.How many whole numbers lie between 33² and 34²?
  30. 30.What is √7744? =
  31. 31.What is √324? =
  32. 32.What is √4489? =
  33. 33.Which of these is a perfect square? (a) 361 (b) 375 (c) 369
  34. 34.What is 54²? =
  35. 35.Which of these is a perfect square? (a) 996 (b) 961 (c) 991
  36. 36.Which of these is a perfect square? (a) 1247 (b) 1284 (c) 1225
  37. 37.What is 81²? =
  38. 38.How many whole numbers lie between 30² and 31²?
  39. 39.Which of these is a perfect square? (a) 344 (b) 330 (c) 324
  40. 40.How many whole numbers lie between 15² and 16²?

Answer key

  1. 75
  2. 10
  3. 37
  4. 5
  5. 169
  6. 97
  7. 54
  8. 8
  9. 34
  10. 2
  11. 55
  12. 10
  13. 54
  14. 441
  15. 1600
  16. 41
  17. 3
  18. 56
  19. 76
  20. 676
  21. 3844
  22. 52
  23. 48
  24. 94
  25. 86
  26. 32
  27. 14
  28. 9604
  29. 66
  30. 88
  31. 18
  32. 67
  33. 361
  34. 2916
  35. 961
  36. 1225
  37. 6561
  38. 60
  39. 324
  40. 30

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