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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 102 · 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 √9409? =
  2. 2.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is 59²? =
  6. 6.What is √6084? =
  7. 7.What is 38²? =
  8. 8.Which of these is a perfect square? (a) 388 (b) 369 (c) 361
  9. 9.A square garden has an area of 256 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 1443 (b) 1387 (c) 1369
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √784? =
  13. 13.What is √8464? =
  14. 14.How many whole numbers lie between 38² and 39²?
  15. 15.What is √4761? =
  16. 16.A square garden has an area of 3481 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  18. 18.What is 75²? =
  19. 19.A square garden has an area of 49 square m. How long is each side (in m)?
  20. 20.What is 29²? =
  21. 21.How many whole numbers lie between 39² and 40²?
  22. 22.How many whole numbers lie between 16² and 17²?
  23. 23.A square garden has an area of 1444 square m. How long is each side (in m)?
  24. 24.A square garden has an area of 2401 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 243 must be divided to get a perfect square?
  26. 26.How many whole numbers lie between 6² and 7²?
  27. 27.A square garden has an area of 676 square m. How long is each side (in m)?
  28. 28.Which of these is a perfect square? (a) 121 (b) 136 (c) 122
  29. 29.How many whole numbers lie between 42² and 43²?
  30. 30.How many whole numbers lie between 26² and 27²?
  31. 31.What is √6400? =
  32. 32.How many whole numbers lie between 34² and 35²?
  33. 33.What is √625? =
  34. 34.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  35. 35.How many whole numbers lie between 8² and 9²?
  36. 36.How many whole numbers lie between 44² and 45²?
  37. 37.How many whole numbers lie between 24² and 25²?
  38. 38.A square garden has an area of 3136 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 197 (b) 196 (c) 210
  40. 40.A square garden has an area of 1936 square m. How long is each side (in m)?

Answer key

  1. 97
  2. 400
  3. 49
  4. 529
  5. 3481
  6. 78
  7. 1444
  8. 361
  9. 16
  10. 1369
  11. 144
  12. 28
  13. 92
  14. 76
  15. 69
  16. 59
  17. 14
  18. 5625
  19. 7
  20. 841
  21. 78
  22. 32
  23. 38
  24. 49
  25. 3
  26. 12
  27. 26
  28. 121
  29. 84
  30. 52
  31. 80
  32. 68
  33. 25
  34. 7
  35. 16
  36. 88
  37. 48
  38. 56
  39. 196
  40. 44

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