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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 146 · 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) 689 (b) 676 (c) 695
  2. 2.Which of these is a perfect square? (a) 441 (b) 448 (c) 468
  3. 3.A square garden has an area of 2500 square m. How long is each side (in m)?
  4. 4.What is 75²? =
  5. 5.What is √676? =
  6. 6.What is √7744? =
  7. 7.How many whole numbers lie between 41² and 42²?
  8. 8.What is 85²? =
  9. 9.What is 37²? =
  10. 10.What is 59²? =
  11. 11.Which of these is a perfect square? (a) 1096 (b) 1147 (c) 1089
  12. 12.How many whole numbers lie between 8² and 9²?
  13. 13.What is the smallest whole number by which 24 must be divided to get a perfect square?
  14. 14.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 2601 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 10² and 11²?
  17. 17.What is the smallest whole number by which 147 must be divided to get a perfect square?
  18. 18.What is 19²? =
  19. 19.What is 12²? =
  20. 20.A square garden has an area of 81 square m. How long is each side (in m)?
  21. 21.What is √5776? =
  22. 22.Which of these is a perfect square? (a) 205 (b) 214 (c) 196
  23. 23.How many whole numbers lie between 21² and 22²?
  24. 24.A square garden has an area of 529 square m. How long is each side (in m)?
  25. 25.What is 18²? =
  26. 26.Which of these is a perfect square? (a) 841 (b) 899 (c) 886
  27. 27.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 29²? =
  29. 29.How many whole numbers lie between 20² and 21²?
  30. 30.How many whole numbers lie between 25² and 26²?
  31. 31.How many whole numbers lie between 17² and 18²?
  32. 32.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is 58²? =
  34. 34.Which of these is a perfect square? (a) 576 (b) 611 (c) 585
  35. 35.Which of these is a perfect square? (a) 729 (b) 763 (c) 740
  36. 36.What is the smallest whole number by which 252 must be divided to get a perfect square?
  37. 37.What is 92²? =
  38. 38.A square garden has an area of 36 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 3481 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 143 (b) 124 (c) 121

Answer key

  1. 676
  2. 441
  3. 50
  4. 5625
  5. 26
  6. 88
  7. 82
  8. 7225
  9. 1369
  10. 3481
  11. 1089
  12. 16
  13. 6
  14. 169
  15. 51
  16. 20
  17. 3
  18. 361
  19. 144
  20. 9
  21. 76
  22. 196
  23. 42
  24. 23
  25. 324
  26. 841
  27. 289
  28. 841
  29. 40
  30. 50
  31. 34
  32. 729
  33. 3364
  34. 576
  35. 729
  36. 7
  37. 8464
  38. 6
  39. 59
  40. 121

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