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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 61 · 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 95²? =
  2. 2.What is √8649? =
  3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 324 square m. How long is each side (in m)?
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 14² and 15²?
  7. 7.What is 29²? =
  8. 8.What is √225? =
  9. 9.What is 86²? =
  10. 10.What is √1521? =
  11. 11.What is √5184? =
  12. 12.What is the smallest whole number by which 75 must be divided to get a perfect square?
  13. 13.What is √1849? =
  14. 14.Which of these is a perfect square? (a) 158 (b) 155 (c) 144
  15. 15.What is 90²? =
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 92²? =
  18. 18.What is √3600? =
  19. 19.What is √9409? =
  20. 20.What is 22²? =
  21. 21.What is √6241? =
  22. 22.How many whole numbers lie between 43² and 44²?
  23. 23.What is the smallest whole number by which 8 must be divided to get a perfect square?
  24. 24.What is 12²? =
  25. 25.What is √441? =
  26. 26.What is 74²? =
  27. 27.What is √3025? =
  28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 89²? =
  30. 30.What is 38²? =
  31. 31.What is 27²? =
  32. 32.What is 69²? =
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 1089 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 1039 (b) 1024 (c) 1080
  36. 36.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  37. 37.How many whole numbers lie between 48² and 49²?
  38. 38.What is 17²? =
  39. 39.How many whole numbers lie between 28² and 29²?
  40. 40.What is the smallest whole number by which 384 must be divided to get a perfect square?

Answer key

  1. 9025
  2. 93
  3. 625
  4. 18
  5. 36
  6. 28
  7. 841
  8. 15
  9. 7396
  10. 39
  11. 72
  12. 3
  13. 43
  14. 144
  15. 8100
  16. 361
  17. 8464
  18. 60
  19. 97
  20. 484
  21. 79
  22. 86
  23. 2
  24. 144
  25. 21
  26. 5476
  27. 55
  28. 196
  29. 7921
  30. 1444
  31. 729
  32. 4761
  33. 25
  34. 33
  35. 1024
  36. 14
  37. 96
  38. 289
  39. 56
  40. 6

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