← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 535 · 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 √6241? =
  2. 2.What is 44²? =
  3. 3.How many whole numbers lie between 26² and 27²?
  4. 4.Which of these is a perfect square? (a) 1225 (b) 1275 (c) 1266
  5. 5.What is √3969? =
  6. 6.What is 65²? =
  7. 7.What is √841? =
  8. 8.Which of these is a perfect square? (a) 625 (b) 632 (c) 666
  9. 9.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 24² and 25²?
  11. 11.What is √1089? =
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is 50²? =
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 144 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 441 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 1296 square m. How long is each side (in m)?
  18. 18.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is √225? =
  20. 20.Which of these is a perfect square? (a) 576 (b) 613 (c) 598
  21. 21.What is the smallest whole number by which 832 must be divided to get a perfect square?
  22. 22.How many whole numbers lie between 45² and 46²?
  23. 23.How many whole numbers lie between 13² and 14²?
  24. 24.Which of these is a perfect square? (a) 361 (b) 396 (c) 397
  25. 25.A square garden has an area of 529 square m. How long is each side (in m)?
  26. 26.What is √1225? =
  27. 27.Which of these is a perfect square? (a) 504 (b) 484 (c) 517
  28. 28.How many whole numbers lie between 18² and 19²?
  29. 29.What is √5041? =
  30. 30.What is the smallest whole number by which 135 must be divided to get a perfect square?
  31. 31.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √9409? =
  33. 33.How many whole numbers lie between 31² and 32²?
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the smallest whole number by which 686 must be divided to get a perfect square?
  36. 36.What is √1296? =
  37. 37.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  38. 38.What is 72²? =
  39. 39.Which of these is a perfect square? (a) 722 (b) 710 (c) 676
  40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 79
  2. 1936
  3. 52
  4. 1225
  5. 63
  6. 4225
  7. 29
  8. 625
  9. 3
  10. 48
  11. 33
  12. 49
  13. 2500
  14. 784
  15. 12
  16. 21
  17. 36
  18. 100
  19. 15
  20. 576
  21. 13
  22. 90
  23. 26
  24. 361
  25. 23
  26. 35
  27. 484
  28. 36
  29. 71
  30. 15
  31. 625
  32. 97
  33. 62
  34. 256
  35. 14
  36. 36
  37. 6
  38. 5184
  39. 676
  40. 289

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