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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 333 · 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 the smallest whole number by which 637 must be divided to get a perfect square?
  2. 2.What is the smallest whole number by which 468 must be divided to get a perfect square?
  3. 3.A square garden has an area of 2809 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 36² and 37²?
  5. 5.What is the smallest whole number by which 54 must be divided to get a perfect square?
  6. 6.What is √5776? =
  7. 7.How many whole numbers lie between 39² and 40²?
  8. 8.Which of these is a perfect square? (a) 1292 (b) 1282 (c) 1225
  9. 9.A square garden has an area of 1156 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  11. 11.What is √7569? =
  12. 12.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  13. 13.A square garden has an area of 2601 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  15. 15.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  16. 16.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 1183 (b) 1156 (c) 1186
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is √7396? =
  20. 20.What is √961? =
  21. 21.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  22. 22.What is √9216? =
  23. 23.What is √4900? =
  24. 24.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 63²? =
  26. 26.How many whole numbers lie between 11² and 12²?
  27. 27.What is √1936? =
  28. 28.What is 18²? =
  29. 29.What is 26²? =
  30. 30.How many whole numbers lie between 30² and 31²?
  31. 31.A square garden has an area of 169 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 1480 (b) 1463 (c) 1444
  33. 33.A square garden has an area of 49 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 289 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 1653 (b) 1646 (c) 1600
  37. 37.A square garden has an area of 1444 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is 97²? =

Answer key

  1. 13
  2. 13
  3. 53
  4. 72
  5. 6
  6. 76
  7. 78
  8. 1225
  9. 34
  10. 13
  11. 87
  12. 6
  13. 51
  14. 5
  15. 10
  16. 13
  17. 1156
  18. 361
  19. 86
  20. 31
  21. 3
  22. 96
  23. 70
  24. 324
  25. 3969
  26. 22
  27. 44
  28. 324
  29. 676
  30. 60
  31. 13
  32. 1444
  33. 7
  34. 64
  35. 17
  36. 1600
  37. 38
  38. 7
  39. 144
  40. 9409

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