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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 174 · 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 80 must be multiplied to get a perfect square?
  2. 2.How many whole numbers lie between 16² and 17²?
  3. 3.What is the smallest whole number by which 343 must be divided to get a perfect square?
  4. 4.What is √5476? =
  5. 5.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  6. 6.A square garden has an area of 324 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 960 must be divided to get a perfect square?
  8. 8.What is 69²? =
  9. 9.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  10. 10.A square garden has an area of 1369 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 3600 square m. How long is each side (in m)?
  13. 13.What is 30²? =
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √8100? =
  16. 16.What is √6724? =
  17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  18. 18.A square garden has an area of 729 square m. How long is each side (in m)?
  19. 19.What is √2809? =
  20. 20.What is √1296? =
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  23. 23.How many whole numbers lie between 30² and 31²?
  24. 24.Which of these is a perfect square? (a) 978 (b) 961 (c) 972
  25. 25.What is √6084? =
  26. 26.A square garden has an area of 1600 square m. How long is each side (in m)?
  27. 27.What is √5929? =
  28. 28.Which of these is a perfect square? (a) 249 (b) 239 (c) 225
  29. 29.How many whole numbers lie between 10² and 11²?
  30. 30.What is the smallest whole number by which 243 must be divided to get a perfect square?
  31. 31.What is 40²? =
  32. 32.What is 91²? =
  33. 33.What is the smallest whole number by which 44 must be divided to get a perfect square?
  34. 34.What is 74²? =
  35. 35.What is 97²? =
  36. 36.Which of these is a perfect square? (a) 100 (b) 115 (c) 118
  37. 37.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  38. 38.How many whole numbers lie between 37² and 38²?
  39. 39.A square garden has an area of 121 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 1348 (b) 1296 (c) 1364

Answer key

  1. 5
  2. 32
  3. 7
  4. 74
  5. 14
  6. 18
  7. 15
  8. 4761
  9. 11
  10. 37
  11. 324
  12. 60
  13. 900
  14. 729
  15. 90
  16. 82
  17. 36
  18. 27
  19. 53
  20. 36
  21. 25
  22. 6
  23. 60
  24. 961
  25. 78
  26. 40
  27. 77
  28. 225
  29. 20
  30. 3
  31. 1600
  32. 8281
  33. 11
  34. 5476
  35. 9409
  36. 100
  37. 10
  38. 74
  39. 11
  40. 1296

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