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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 270 · 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 196 square m. How long is each side (in m)?
  2. 2.What is the smallest whole number by which 20 must be divided to get a perfect square?
  3. 3.How many whole numbers lie between 8² and 9²?
  4. 4.Which of these is a perfect square? (a) 860 (b) 841 (c) 861
  5. 5.What is √6724? =
  6. 6.What is √361? =
  7. 7.Which of these is a perfect square? (a) 1551 (b) 1599 (c) 1521
  8. 8.How many whole numbers lie between 12² and 13²?
  9. 9.A square garden has an area of 3600 square m. How long is each side (in m)?
  10. 10.A square garden has an area of 3249 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 14² and 15²?
  14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is 43²? =
  16. 16.A square garden has an area of 1444 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 1521 square m. How long is each side (in m)?
  18. 18.What is √4356? =
  19. 19.Which of these is a perfect square? (a) 1068 (b) 1047 (c) 1024
  20. 20.What is the smallest whole number by which 28 must be divided to get a perfect square?
  21. 21.What is √225? =
  22. 22.What is √6561? =
  23. 23.How many whole numbers lie between 35² and 36²?
  24. 24.What is √5184? =
  25. 25.What is 19²? =
  26. 26.What is the smallest whole number by which 117 must be divided to get a perfect square?
  27. 27.A square garden has an area of 784 square m. How long is each side (in m)?
  28. 28.What is √2704? =
  29. 29.What is √256? =
  30. 30.What is 11²? =
  31. 31.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  32. 32.What is √400? =
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is √3721? =
  35. 35.What is √529? =
  36. 36.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  37. 37.Which of these is a perfect square? (a) 196 (b) 204 (c) 210
  38. 38.What is √3136? =
  39. 39.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 522 (b) 484 (c) 488

Answer key

  1. 14
  2. 5
  3. 16
  4. 841
  5. 82
  6. 19
  7. 1521
  8. 24
  9. 60
  10. 57
  11. 49
  12. 900
  13. 28
  14. 289
  15. 1849
  16. 38
  17. 39
  18. 66
  19. 1024
  20. 7
  21. 15
  22. 81
  23. 70
  24. 72
  25. 361
  26. 13
  27. 28
  28. 52
  29. 16
  30. 121
  31. 3
  32. 20
  33. 361
  34. 61
  35. 23
  36. 576
  37. 196
  38. 56
  39. 6
  40. 484

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