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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 684 · 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 20²? =
  2. 2.A square garden has an area of 2025 square m. How long is each side (in m)?
  3. 3.Which of these is a perfect square? (a) 484 (b) 504 (c) 491
  4. 4.How many whole numbers lie between 5² and 6²?
  5. 5.What is 53²? =
  6. 6.What is √729? =
  7. 7.What is √1156? =
  8. 8.What is the smallest whole number by which 27 must be divided to get a perfect square?
  9. 9.How many whole numbers lie between 11² and 12²?
  10. 10.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  11. 11.A square garden has an area of 81 square m. How long is each side (in m)?
  12. 12.What is √6724? =
  13. 13.What is √4900? =
  14. 14.How many whole numbers lie between 20² and 21²?
  15. 15.What is the smallest whole number by which 250 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  17. 17.What is 68²? =
  18. 18.A square garden has an area of 1024 square m. How long is each side (in m)?
  19. 19.What is 85²? =
  20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 34² and 35²?
  22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √3249? =
  24. 24.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 76²? =
  26. 26.A square garden has an area of 1156 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  28. 28.Which of these is a perfect square? (a) 728 (b) 676 (c) 707
  29. 29.What is √121? =
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  31. 31.Which of these is a perfect square? (a) 1024 (b) 1037 (c) 1084
  32. 32.What is the smallest whole number by which 60 must be divided to get a perfect square?
  33. 33.What is 61²? =
  34. 34.What is √8281? =
  35. 35.What is the smallest whole number by which 490 must be divided to get a perfect square?
  36. 36.What is 11²? =
  37. 37.What is 43²? =
  38. 38.What is the smallest whole number by which 8 must be divided to get a perfect square?
  39. 39.A square garden has an area of 1521 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 198 (b) 223 (c) 196

Answer key

  1. 400
  2. 45
  3. 484
  4. 10
  5. 2809
  6. 27
  7. 34
  8. 3
  9. 22
  10. 400
  11. 9
  12. 82
  13. 70
  14. 40
  15. 10
  16. 13
  17. 4624
  18. 32
  19. 7225
  20. 20
  21. 68
  22. 25
  23. 57
  24. 196
  25. 5776
  26. 34
  27. 256
  28. 676
  29. 11
  30. 144
  31. 1024
  32. 15
  33. 3721
  34. 91
  35. 10
  36. 121
  37. 1849
  38. 2
  39. 39
  40. 196

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