← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 654 · 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 √400? =
  2. 2.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  3. 3.What is 19²? =
  4. 4.What is √2601? =
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √2209? =
  7. 7.What is √1936? =
  8. 8.Which of these is a perfect square? (a) 759 (b) 729 (c) 780
  9. 9.What is √7056? =
  10. 10.What is 60²? =
  11. 11.Which of these is a perfect square? (a) 203 (b) 214 (c) 196
  12. 12.A square garden has an area of 1024 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 704 (b) 676 (c) 683
  15. 15.Which of these is a perfect square? (a) 1336 (b) 1296 (c) 1329
  16. 16.What is 52²? =
  17. 17.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  18. 18.How many whole numbers lie between 25² and 26²?
  19. 19.What is 21²? =
  20. 20.What is √6889? =
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √1681? =
  23. 23.Which of these is a perfect square? (a) 784 (b) 813 (c) 833
  24. 24.Which of these is a perfect square? (a) 607 (b) 599 (c) 576
  25. 25.What is √2704? =
  26. 26.Which of these is a perfect square? (a) 176 (b) 194 (c) 169
  27. 27.What is √144? =
  28. 28.What is the smallest whole number by which 126 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 21² and 22²?
  30. 30.Which of these is a perfect square? (a) 106 (b) 101 (c) 100
  31. 31.What is 79²? =
  32. 32.A square garden has an area of 225 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 27² and 28²?
  34. 34.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  35. 35.A square garden has an area of 1296 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 12² and 13²?
  37. 37.What is √4225? =
  38. 38.Which of these is a perfect square? (a) 415 (b) 400 (c) 406
  39. 39.What is the smallest whole number by which 396 must be divided to get a perfect square?
  40. 40.How many whole numbers lie between 8² and 9²?

Answer key

  1. 20
  2. 3
  3. 361
  4. 51
  5. 289
  6. 47
  7. 44
  8. 729
  9. 84
  10. 3600
  11. 196
  12. 32
  13. 121
  14. 676
  15. 1296
  16. 2704
  17. 196
  18. 50
  19. 441
  20. 83
  21. 169
  22. 41
  23. 784
  24. 576
  25. 52
  26. 169
  27. 12
  28. 14
  29. 42
  30. 100
  31. 6241
  32. 15
  33. 54
  34. 3
  35. 36
  36. 24
  37. 65
  38. 400
  39. 11
  40. 16

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