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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 592 · 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.How many whole numbers lie between 32² and 33²?
  2. 2.What is √3364? =
  3. 3.What is √784? =
  4. 4.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 24² and 25²?
  6. 6.A square garden has an area of 3364 square m. How long is each side (in m)?
  7. 7.How many whole numbers lie between 39² and 40²?
  8. 8.What is √2401? =
  9. 9.How many whole numbers lie between 36² and 37²?
  10. 10.A square garden has an area of 625 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 71²? =
  13. 13.What is 54²? =
  14. 14.Which of these is a perfect square? (a) 448 (b) 450 (c) 441
  15. 15.How many whole numbers lie between 15² and 16²?
  16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  18. 18.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √3600? =
  21. 21.Which of these is a perfect square? (a) 1270 (b) 1287 (c) 1225
  22. 22.What is √3969? =
  23. 23.What is 26²? =
  24. 24.What is 19²? =
  25. 25.What is √900? =
  26. 26.What is √3481? =
  27. 27.What is √1156? =
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  29. 29.Which of these is a perfect square? (a) 738 (b) 729 (c) 775
  30. 30.What is √7744? =
  31. 31.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √121? =
  33. 33.Which of these is a perfect square? (a) 1069 (b) 1059 (c) 1024
  34. 34.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 212 (b) 211 (c) 196
  37. 37.Which of these is a perfect square? (a) 510 (b) 484 (c) 505
  38. 38.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  39. 39.What is the smallest whole number by which 448 must be divided to get a perfect square?
  40. 40.What is √441? =

Answer key

  1. 64
  2. 58
  3. 28
  4. 484
  5. 48
  6. 58
  7. 78
  8. 49
  9. 72
  10. 25
  11. 324
  12. 5041
  13. 2916
  14. 441
  15. 30
  16. 225
  17. 3
  18. 6
  19. 36
  20. 60
  21. 1225
  22. 63
  23. 676
  24. 361
  25. 30
  26. 59
  27. 34
  28. 100
  29. 729
  30. 88
  31. 900
  32. 11
  33. 1024
  34. 7
  35. 121
  36. 196
  37. 484
  38. 11
  39. 7
  40. 21

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