← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 209 · 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.A square garden has an area of 2304 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 256 (b) 269 (c) 258
  3. 3.What is √1849? =
  4. 4.Which of these is a perfect square? (a) 1189 (b) 1156 (c) 1220
  5. 5.What is 39²? =
  6. 6.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 848 (b) 854 (c) 841
  8. 8.What is √8464? =
  9. 9.A square garden has an area of 169 square m. How long is each side (in m)?
  10. 10.How many whole numbers lie between 48² and 49²?
  11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 80²? =
  13. 13.Which of these is a perfect square? (a) 1244 (b) 1225 (c) 1270
  14. 14.What is 72²? =
  15. 15.Which of these is a perfect square? (a) 909 (b) 921 (c) 900
  16. 16.How many whole numbers lie between 6² and 7²?
  17. 17.How many whole numbers lie between 22² and 23²?
  18. 18.Which of these is a perfect square? (a) 1426 (b) 1369 (c) 1405
  19. 19.What is the smallest whole number by which 27 must be divided to get a perfect square?
  20. 20.How many whole numbers lie between 35² and 36²?
  21. 21.A square garden has an area of 1369 square m. How long is each side (in m)?
  22. 22.How many whole numbers lie between 24² and 25²?
  23. 23.A square garden has an area of 100 square m. How long is each side (in m)?
  24. 24.How many whole numbers lie between 11² and 12²?
  25. 25.What is 25²? =
  26. 26.Which of these is a perfect square? (a) 202 (b) 196 (c) 200
  27. 27.What is √6724? =
  28. 28.Which of these is a perfect square? (a) 361 (b) 382 (c) 374
  29. 29.What is 59²? =
  30. 30.How many whole numbers lie between 39² and 40²?
  31. 31.What is √7225? =
  32. 32.A square garden has an area of 289 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  34. 34.What is √484? =
  35. 35.What is 40²? =
  36. 36.What is √6561? =
  37. 37.What is 79²? =
  38. 38.What is √961? =
  39. 39.What is 28²? =
  40. 40.How many whole numbers lie between 40² and 41²?

Answer key

  1. 48
  2. 256
  3. 43
  4. 1156
  5. 1521
  6. 676
  7. 841
  8. 92
  9. 13
  10. 96
  11. 196
  12. 6400
  13. 1225
  14. 5184
  15. 900
  16. 12
  17. 44
  18. 1369
  19. 3
  20. 70
  21. 37
  22. 48
  23. 10
  24. 22
  25. 625
  26. 196
  27. 82
  28. 361
  29. 3481
  30. 78
  31. 85
  32. 17
  33. 2
  34. 22
  35. 1600
  36. 81
  37. 6241
  38. 31
  39. 784
  40. 80

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