← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 406 · 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) 1225 (b) 1285 (c) 1276
  2. 2.Which of these is a perfect square? (a) 1444 (b) 1452 (c) 1501
  3. 3.Which of these is a perfect square? (a) 1110 (b) 1089 (c) 1092
  4. 4.What is √2025? =
  5. 5.What is 42²? =
  6. 6.What is 14²? =
  7. 7.What is √3600? =
  8. 8.What is 60²? =
  9. 9.Which of these is a perfect square? (a) 1600 (b) 1630 (c) 1606
  10. 10.What is √1369? =
  11. 11.How many whole numbers lie between 13² and 14²?
  12. 12.How many whole numbers lie between 32² and 33²?
  13. 13.What is 12²? =
  14. 14.How many whole numbers lie between 31² and 32²?
  15. 15.How many whole numbers lie between 38² and 39²?
  16. 16.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  17. 17.What is √144? =
  18. 18.A square garden has an area of 1849 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  20. 20.What is √4225? =
  21. 21.What is √1849? =
  22. 22.What is √2809? =
  23. 23.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the smallest whole number by which 99 must be divided to get a perfect square?
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  26. 26.How many whole numbers lie between 18² and 19²?
  27. 27.How many whole numbers lie between 5² and 6²?
  28. 28.Which of these is a perfect square? (a) 225 (b) 251 (c) 248
  29. 29.What is √2704? =
  30. 30.Which of these is a perfect square? (a) 961 (b) 970 (c) 1002
  31. 31.How many whole numbers lie between 8² and 9²?
  32. 32.What is 57²? =
  33. 33.What is the smallest whole number by which 294 must be divided to get a perfect square?
  34. 34.What is √961? =
  35. 35.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 12 must be divided to get a perfect square?
  37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √8281? =
  39. 39.What is 21²? =
  40. 40.A square garden has an area of 2116 square m. How long is each side (in m)?

Answer key

  1. 1225
  2. 1444
  3. 1089
  4. 45
  5. 1764
  6. 196
  7. 60
  8. 3600
  9. 1600
  10. 37
  11. 26
  12. 64
  13. 144
  14. 62
  15. 76
  16. 3
  17. 12
  18. 43
  19. 2
  20. 65
  21. 43
  22. 53
  23. 361
  24. 11
  25. 100
  26. 36
  27. 10
  28. 225
  29. 52
  30. 961
  31. 16
  32. 3249
  33. 6
  34. 31
  35. 13
  36. 3
  37. 289
  38. 91
  39. 441
  40. 46

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