← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 474 · 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 5 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 5² and 6²?
  4. 4.How many whole numbers lie between 18² and 19²?
  5. 5.A square garden has an area of 1849 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 2401 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 676 square m. How long is each side (in m)?
  8. 8.What is 11²? =
  9. 9.What is √8649? =
  10. 10.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  11. 11.A square garden has an area of 225 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 221 (b) 205 (c) 196
  13. 13.A square garden has an area of 1225 square m. How long is each side (in m)?
  14. 14.What is √4096? =
  15. 15.A square garden has an area of 3600 square m. How long is each side (in m)?
  16. 16.What is √4489? =
  17. 17.What is √1521? =
  18. 18.What is √6241? =
  19. 19.What is 14²? =
  20. 20.A square garden has an area of 1764 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 841 (b) 898 (c) 884
  22. 22.What is 67²? =
  23. 23.What is √5041? =
  24. 24.A square garden has an area of 400 square m. How long is each side (in m)?
  25. 25.Which of these is a perfect square? (a) 1262 (b) 1229 (c) 1225
  26. 26.A square garden has an area of 64 square m. How long is each side (in m)?
  27. 27.What is √3025? =
  28. 28.What is √7225? =
  29. 29.A square garden has an area of 2500 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 976 (b) 984 (c) 961
  31. 31.A square garden has an area of 25 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 252 must be divided to get a perfect square?
  33. 33.What is √5929? =
  34. 34.What is 81²? =
  35. 35.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 216 must be divided to get a perfect square?
  37. 37.A square garden has an area of 1936 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 900 (b) 952 (c) 911
  39. 39.What is √9604? =
  40. 40.Which of these is a perfect square? (a) 1600 (b) 1606 (c) 1653

Answer key

  1. 25
  2. 196
  3. 10
  4. 36
  5. 43
  6. 49
  7. 26
  8. 121
  9. 93
  10. 6
  11. 15
  12. 196
  13. 35
  14. 64
  15. 60
  16. 67
  17. 39
  18. 79
  19. 196
  20. 42
  21. 841
  22. 4489
  23. 71
  24. 20
  25. 1225
  26. 8
  27. 55
  28. 85
  29. 50
  30. 961
  31. 5
  32. 7
  33. 77
  34. 6561
  35. 676
  36. 6
  37. 44
  38. 900
  39. 98
  40. 1600

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