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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 365 · 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.A square garden has an area of 484 square m. How long is each side (in m)?
  2. 2.What is 98²? =
  3. 3.What is √441? =
  4. 4.A square garden has an area of 1225 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 256 square m. How long is each side (in m)?
  6. 6.What is √961? =
  7. 7.How many whole numbers lie between 40² and 41²?
  8. 8.How many whole numbers lie between 47² and 48²?
  9. 9.A square garden has an area of 361 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  11. 11.What is √484? =
  12. 12.A square garden has an area of 1296 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is √1089? =
  15. 15.What is the smallest whole number by which 245 must be divided to get a perfect square?
  16. 16.What is 31²? =
  17. 17.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  18. 18.Which of these is a perfect square? (a) 625 (b) 636 (c) 658
  19. 19.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  20. 20.What is √6561? =
  21. 21.Which of these is a perfect square? (a) 821 (b) 814 (c) 784
  22. 22.How many whole numbers lie between 35² and 36²?
  23. 23.Which of these is a perfect square? (a) 247 (b) 225 (c) 227
  24. 24.How many whole numbers lie between 48² and 49²?
  25. 25.What is √729? =
  26. 26.How many whole numbers lie between 18² and 19²?
  27. 27.Which of these is a perfect square? (a) 601 (b) 576 (c) 579
  28. 28.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  29. 29.How many whole numbers lie between 25² and 26²?
  30. 30.A square garden has an area of 196 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  32. 32.What is √2401? =
  33. 33.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  34. 34.What is √900? =
  35. 35.What is 64²? =
  36. 36.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 49²? =
  38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is 87²? =

Answer key

  1. 22
  2. 9604
  3. 21
  4. 35
  5. 16
  6. 31
  7. 80
  8. 94
  9. 19
  10. 10
  11. 22
  12. 36
  13. 256
  14. 33
  15. 5
  16. 961
  17. 3
  18. 625
  19. 3
  20. 81
  21. 784
  22. 70
  23. 225
  24. 96
  25. 27
  26. 36
  27. 576
  28. 900
  29. 50
  30. 14
  31. 3
  32. 49
  33. 10
  34. 30
  35. 4096
  36. 121
  37. 2401
  38. 36
  39. 289
  40. 7569

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