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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 109 · 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) 1648 (b) 1644 (c) 1600
  2. 2.How many whole numbers lie between 10² and 11²?
  3. 3.What is √5929? =
  4. 4.What is √2809? =
  5. 5.What is 57²? =
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 48² and 49²?
  8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √6400? =
  10. 10.How many whole numbers lie between 22² and 23²?
  11. 11.What is the smallest whole number by which 252 must be divided to get a perfect square?
  12. 12.What is √1156? =
  13. 13.What is the smallest whole number by which 32 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 145 (b) 144 (c) 168
  15. 15.What is 35²? =
  16. 16.How many whole numbers lie between 37² and 38²?
  17. 17.What is √324? =
  18. 18.Which of these is a perfect square? (a) 112 (b) 118 (c) 100
  19. 19.What is 40²? =
  20. 20.What is the smallest whole number by which 117 must be divided to get a perfect square?
  21. 21.What is 41²? =
  22. 22.What is √3025? =
  23. 23.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 400 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 18 must be divided to get a perfect square?
  26. 26.A square garden has an area of 361 square m. How long is each side (in m)?
  27. 27.What is 24²? =
  28. 28.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √144? =
  30. 30.A square garden has an area of 1225 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 1089 (b) 1097 (c) 1093
  32. 32.What is 47²? =
  33. 33.Which of these is a perfect square? (a) 641 (b) 661 (c) 625
  34. 34.How many whole numbers lie between 31² and 32²?
  35. 35.What is the smallest whole number by which 343 must be divided to get a perfect square?
  36. 36.What is 37²? =
  37. 37.What is √4489? =
  38. 38.What is the smallest whole number by which 567 must be divided to get a perfect square?
  39. 39.What is the smallest whole number by which 12 must be divided to get a perfect square?
  40. 40.What is √2209? =

Answer key

  1. 1600
  2. 20
  3. 77
  4. 53
  5. 3249
  6. 289
  7. 96
  8. 361
  9. 80
  10. 44
  11. 7
  12. 34
  13. 2
  14. 144
  15. 1225
  16. 74
  17. 18
  18. 100
  19. 1600
  20. 13
  21. 1681
  22. 55
  23. 2
  24. 20
  25. 2
  26. 19
  27. 576
  28. 256
  29. 12
  30. 35
  31. 1089
  32. 2209
  33. 625
  34. 62
  35. 7
  36. 1369
  37. 67
  38. 7
  39. 3
  40. 47

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