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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 264 · 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.A square garden has an area of 2809 square m. How long is each side (in m)?
  2. 2.What is √4624? =
  3. 3.What is √4761? =
  4. 4.What is 59²? =
  5. 5.How many whole numbers lie between 41² and 42²?
  6. 6.Which of these is a perfect square? (a) 565 (b) 543 (c) 529
  7. 7.What is 94²? =
  8. 8.A square garden has an area of 25 square m. How long is each side (in m)?
  9. 9.What is 42²? =
  10. 10.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  11. 11.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  12. 12.What is √1225? =
  13. 13.What is √1764? =
  14. 14.A square garden has an area of 3136 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 121 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 841 (b) 867 (c) 884
  18. 18.What is 65²? =
  19. 19.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 960 must be divided to get a perfect square?
  21. 21.What is 79²? =
  22. 22.What is 38²? =
  23. 23.What is 19²? =
  24. 24.What is the smallest whole number by which 325 must be divided to get a perfect square?
  25. 25.What is 61²? =
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √6724? =
  28. 28.What is √484? =
  29. 29.What is 85²? =
  30. 30.Which of these is a perfect square? (a) 370 (b) 390 (c) 361
  31. 31.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  32. 32.What is 26²? =
  33. 33.How many whole numbers lie between 22² and 23²?
  34. 34.How many whole numbers lie between 13² and 14²?
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 34²? =
  37. 37.Which of these is a perfect square? (a) 1385 (b) 1372 (c) 1369
  38. 38.What is √2704? =
  39. 39.A square garden has an area of 1156 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 509 (b) 527 (c) 484

Answer key

  1. 53
  2. 68
  3. 69
  4. 3481
  5. 82
  6. 529
  7. 8836
  8. 5
  9. 1764
  10. 13
  11. 7
  12. 35
  13. 42
  14. 56
  15. 11
  16. 3
  17. 841
  18. 4225
  19. 729
  20. 15
  21. 6241
  22. 1444
  23. 361
  24. 13
  25. 3721
  26. 256
  27. 82
  28. 22
  29. 7225
  30. 361
  31. 3
  32. 676
  33. 44
  34. 26
  35. 324
  36. 1156
  37. 1369
  38. 52
  39. 34
  40. 484

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