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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 339 · 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 sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  2. 2.A square garden has an area of 1849 square m. How long is each side (in m)?
  3. 3.What is √576? =
  4. 4.How many whole numbers lie between 23² and 24²?
  5. 5.What is 59²? =
  6. 6.How many whole numbers lie between 41² and 42²?
  7. 7.Which of these is a perfect square? (a) 1659 (b) 1600 (c) 1674
  8. 8.What is 28²? =
  9. 9.What is 79²? =
  10. 10.What is √7569? =
  11. 11.A square garden has an area of 529 square m. How long is each side (in m)?
  12. 12.What is √4624? =
  13. 13.A square garden has an area of 81 square m. How long is each side (in m)?
  14. 14.How many whole numbers lie between 44² and 45²?
  15. 15.A square garden has an area of 484 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 27² and 28²?
  17. 17.A square garden has an area of 3136 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 26² and 27²?
  19. 19.What is √1156? =
  20. 20.What is √2401? =
  21. 21.What is the smallest whole number by which 20 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 161 (b) 162 (c) 144
  23. 23.What is 83²? =
  24. 24.A square garden has an area of 225 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  26. 26.What is √1369? =
  27. 27.A square garden has an area of 400 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 35² and 36²?
  29. 29.A square garden has an area of 1369 square m. How long is each side (in m)?
  30. 30.What is 55²? =
  31. 31.What is 86²? =
  32. 32.What is √144? =
  33. 33.What is 35²? =
  34. 34.What is the smallest whole number by which 252 must be divided to get a perfect square?
  35. 35.How many whole numbers lie between 9² and 10²?
  36. 36.What is the smallest whole number by which 32 must be divided to get a perfect square?
  37. 37.What is √9025? =
  38. 38.A square garden has an area of 1600 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 144 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 117 must be multiplied to get a perfect square?

Answer key

  1. 324
  2. 43
  3. 24
  4. 46
  5. 3481
  6. 82
  7. 1600
  8. 784
  9. 6241
  10. 87
  11. 23
  12. 68
  13. 9
  14. 88
  15. 22
  16. 54
  17. 56
  18. 52
  19. 34
  20. 49
  21. 5
  22. 144
  23. 6889
  24. 15
  25. 5
  26. 37
  27. 20
  28. 70
  29. 37
  30. 3025
  31. 7396
  32. 12
  33. 1225
  34. 7
  35. 18
  36. 2
  37. 95
  38. 40
  39. 12
  40. 13

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