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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 311 · 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 12 must be divided to get a perfect square?
  2. 2.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 28² and 29²?
  4. 4.How many whole numbers lie between 15² and 16²?
  5. 5.How many whole numbers lie between 22² and 23²?
  6. 6.What is √5329? =
  7. 7.What is 49²? =
  8. 8.What is 78²? =
  9. 9.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  10. 10.How many whole numbers lie between 9² and 10²?
  11. 11.How many whole numbers lie between 50² and 51²?
  12. 12.What is √4225? =
  13. 13.A square garden has an area of 1369 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 56 must be divided to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 144 (b) 161 (c) 168
  16. 16.A square garden has an area of 729 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 3600 square m. How long is each side (in m)?
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  19. 19.A square garden has an area of 25 square m. How long is each side (in m)?
  20. 20.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 289 square m. How long is each side (in m)?
  22. 22.What is √4096? =
  23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  25. 25.How many whole numbers lie between 7² and 8²?
  26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √121? =
  28. 28.What is √3721? =
  29. 29.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 24² and 25²?
  31. 31.How many whole numbers lie between 6² and 7²?
  32. 32.A square garden has an area of 81 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 50 must be divided to get a perfect square?
  34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 26²? =
  36. 36.What is 14²? =
  37. 37.What is √1849? =
  38. 38.What is 35²? =
  39. 39.Which of these is a perfect square? (a) 576 (b) 608 (c) 593
  40. 40.What is 94²? =

Answer key

  1. 3
  2. 400
  3. 56
  4. 30
  5. 44
  6. 73
  7. 2401
  8. 6084
  9. 36
  10. 18
  11. 100
  12. 65
  13. 37
  14. 14
  15. 144
  16. 27
  17. 60
  18. 81
  19. 5
  20. 11
  21. 17
  22. 64
  23. 576
  24. 11
  25. 14
  26. 49
  27. 11
  28. 61
  29. 529
  30. 48
  31. 12
  32. 9
  33. 2
  34. 676
  35. 676
  36. 196
  37. 43
  38. 1225
  39. 576
  40. 8836

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