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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 26 · 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 2601 square m. How long is each side (in m)?
  2. 2.A square garden has an area of 1156 square m. How long is each side (in m)?
  3. 3.How many whole numbers lie between 16² and 17²?
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 1296 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  8. 8.How many whole numbers lie between 25² and 26²?
  9. 9.A square garden has an area of 841 square m. How long is each side (in m)?
  10. 10.How many whole numbers lie between 40² and 41²?
  11. 11.What is 34²? =
  12. 12.Which of these is a perfect square? (a) 324 (b) 333 (c) 344
  13. 13.What is √4225? =
  14. 14.What is 33²? =
  15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is √4356? =
  20. 20.How many whole numbers lie between 49² and 50²?
  21. 21.A square garden has an area of 484 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 539 must be divided to get a perfect square?
  23. 23.What is √6084? =
  24. 24.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  25. 25.What is 60²? =
  26. 26.What is √361? =
  27. 27.A square garden has an area of 2209 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 50² and 51²?
  29. 29.What is √1089? =
  30. 30.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √3249? =
  32. 32.What is the smallest whole number by which 320 must be divided to get a perfect square?
  33. 33.How many whole numbers lie between 30² and 31²?
  34. 34.What is √6241? =
  35. 35.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  36. 36.What is √4489? =
  37. 37.How many whole numbers lie between 38² and 39²?
  38. 38.What is √1444? =
  39. 39.A square garden has an area of 1764 square m. How long is each side (in m)?
  40. 40.What is √784? =

Answer key

  1. 51
  2. 34
  3. 32
  4. 121
  5. 36
  6. 100
  7. 10
  8. 50
  9. 29
  10. 80
  11. 1156
  12. 324
  13. 65
  14. 1089
  15. 225
  16. 49
  17. 25
  18. 289
  19. 66
  20. 98
  21. 22
  22. 11
  23. 78
  24. 5
  25. 3600
  26. 19
  27. 47
  28. 100
  29. 33
  30. 676
  31. 57
  32. 5
  33. 60
  34. 79
  35. 5
  36. 67
  37. 76
  38. 38
  39. 42
  40. 28

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