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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 147 · 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.Which of these is a perfect square? (a) 542 (b) 567 (c) 529
  2. 2.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  3. 3.What is √6400? =
  4. 4.What is 91²? =
  5. 5.What is 79²? =
  6. 6.What is 89²? =
  7. 7.A square garden has an area of 1225 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 150 must be divided to get a perfect square?
  9. 9.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 35²? =
  12. 12.A square garden has an area of 2704 square m. How long is each side (in m)?
  13. 13.What is 18²? =
  14. 14.What is 40²? =
  15. 15.A square garden has an area of 841 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 1849 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 100 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 15² and 16²?
  19. 19.What is the smallest whole number by which 176 must be divided to get a perfect square?
  20. 20.What is √1024? =
  21. 21.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  22. 22.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  23. 23.A square garden has an area of 49 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 56 must be divided to get a perfect square?
  25. 25.A square garden has an area of 1600 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 6² and 7²?
  27. 27.What is √6724? =
  28. 28.How many whole numbers lie between 40² and 41²?
  29. 29.How many whole numbers lie between 34² and 35²?
  30. 30.What is 95²? =
  31. 31.What is √3600? =
  32. 32.What is the smallest whole number by which 162 must be divided to get a perfect square?
  33. 33.A square garden has an area of 625 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  35. 35.What is the smallest whole number by which 810 must be divided to get a perfect square?
  36. 36.What is 59²? =
  37. 37.What is √8281? =
  38. 38.How many whole numbers lie between 10² and 11²?
  39. 39.How many whole numbers lie between 19² and 20²?
  40. 40.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 529
  2. 13
  3. 80
  4. 8281
  5. 6241
  6. 7921
  7. 35
  8. 6
  9. 5
  10. 400
  11. 1225
  12. 52
  13. 324
  14. 1600
  15. 29
  16. 43
  17. 10
  18. 30
  19. 11
  20. 32
  21. 13
  22. 3
  23. 7
  24. 14
  25. 40
  26. 12
  27. 82
  28. 80
  29. 68
  30. 9025
  31. 60
  32. 2
  33. 25
  34. 11
  35. 10
  36. 3481
  37. 91
  38. 20
  39. 38
  40. 225

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