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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 327 · 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 sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is 27²? =
  3. 3.Which of these is a perfect square? (a) 884 (b) 852 (c) 841
  4. 4.How many whole numbers lie between 37² and 38²?
  5. 5.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  6. 6.How many whole numbers lie between 20² and 21²?
  7. 7.A square garden has an area of 361 square m. How long is each side (in m)?
  8. 8.What is √1024? =
  9. 9.What is √2401? =
  10. 10.What is √5929? =
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 48² and 49²?
  13. 13.What is √1089? =
  14. 14.What is √8836? =
  15. 15.What is √3481? =
  16. 16.What is 86²? =
  17. 17.Which of these is a perfect square? (a) 529 (b) 537 (c) 541
  18. 18.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  19. 19.What is √361? =
  20. 20.What is 19²? =
  21. 21.What is 95²? =
  22. 22.How many whole numbers lie between 30² and 31²?
  23. 23.What is 60²? =
  24. 24.What is 74²? =
  25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  26. 26.Which of these is a perfect square? (a) 715 (b) 676 (c) 710
  27. 27.What is the smallest whole number by which 52 must be divided to get a perfect square?
  28. 28.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  29. 29.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  32. 32.Which of these is a perfect square? (a) 513 (b) 484 (c) 516
  33. 33.What is 87²? =
  34. 34.How many whole numbers lie between 14² and 15²?
  35. 35.What is √3600? =
  36. 36.A square garden has an area of 121 square m. How long is each side (in m)?
  37. 37.What is √441? =
  38. 38.What is the smallest whole number by which 567 must be divided to get a perfect square?
  39. 39.How many whole numbers lie between 13² and 14²?
  40. 40.What is 24²? =

Answer key

  1. 900
  2. 729
  3. 841
  4. 74
  5. 5
  6. 40
  7. 19
  8. 32
  9. 49
  10. 77
  11. 484
  12. 96
  13. 33
  14. 94
  15. 59
  16. 7396
  17. 529
  18. 10
  19. 19
  20. 361
  21. 9025
  22. 60
  23. 3600
  24. 5476
  25. 25
  26. 676
  27. 13
  28. 14
  29. 169
  30. 3
  31. 361
  32. 484
  33. 7569
  34. 28
  35. 60
  36. 11
  37. 21
  38. 7
  39. 26
  40. 576

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