← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 498 · 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) 387 (b) 361 (c) 370
  2. 2.How many whole numbers lie between 15² and 16²?
  3. 3.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  4. 4.What is √2916? =
  5. 5.Which of these is a perfect square? (a) 324 (b) 360 (c) 341
  6. 6.Which of these is a perfect square? (a) 852 (b) 841 (c) 859
  7. 7.Which of these is a perfect square? (a) 1600 (b) 1624 (c) 1636
  8. 8.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  9. 9.How many whole numbers lie between 25² and 26²?
  10. 10.What is √7744? =
  11. 11.A square garden has an area of 2500 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 1381 (b) 1433 (c) 1369
  13. 13.A square garden has an area of 256 square m. How long is each side (in m)?
  14. 14.How many whole numbers lie between 8² and 9²?
  15. 15.What is 49²? =
  16. 16.What is √5776? =
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  19. 19.What is √324? =
  20. 20.What is 91²? =
  21. 21.A square garden has an area of 2025 square m. How long is each side (in m)?
  22. 22.What is 30²? =
  23. 23.What is √9409? =
  24. 24.What is 34²? =
  25. 25.A square garden has an area of 100 square m. How long is each side (in m)?
  26. 26.What is √2809? =
  27. 27.What is √8100? =
  28. 28.What is √625? =
  29. 29.What is the smallest whole number by which 375 must be divided to get a perfect square?
  30. 30.What is √5476? =
  31. 31.What is 25²? =
  32. 32.How many whole numbers lie between 32² and 33²?
  33. 33.What is √3969? =
  34. 34.Which of these is a perfect square? (a) 663 (b) 659 (c) 625
  35. 35.How many whole numbers lie between 27² and 28²?
  36. 36.A square garden has an area of 2809 square m. How long is each side (in m)?
  37. 37.Which of these is a perfect square? (a) 1149 (b) 1124 (c) 1089
  38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √121? =
  40. 40.A square garden has an area of 289 square m. How long is each side (in m)?

Answer key

  1. 361
  2. 30
  3. 10
  4. 54
  5. 324
  6. 841
  7. 1600
  8. 6
  9. 50
  10. 88
  11. 50
  12. 1369
  13. 16
  14. 16
  15. 2401
  16. 76
  17. 289
  18. 15
  19. 18
  20. 8281
  21. 45
  22. 900
  23. 97
  24. 1156
  25. 10
  26. 53
  27. 90
  28. 25
  29. 15
  30. 74
  31. 625
  32. 64
  33. 63
  34. 625
  35. 54
  36. 53
  37. 1089
  38. 81
  39. 11
  40. 17

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