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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 356 · 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 47² and 48²?
  2. 2.Which of these is a perfect square? (a) 529 (b) 566 (c) 548
  3. 3.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  4. 4.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 1010 (b) 961 (c) 987
  6. 6.What is √9216? =
  7. 7.Which of these is a perfect square? (a) 699 (b) 718 (c) 676
  8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 240 (b) 229 (c) 225
  10. 10.What is √1936? =
  11. 11.What is the smallest whole number by which 40 must be divided to get a perfect square?
  12. 12.Which of these is a perfect square? (a) 262 (b) 263 (c) 256
  13. 13.Which of these is a perfect square? (a) 296 (b) 291 (c) 289
  14. 14.A square garden has an area of 2500 square m. How long is each side (in m)?
  15. 15.What is 21²? =
  16. 16.What is √4356? =
  17. 17.Which of these is a perfect square? (a) 463 (b) 441 (c) 472
  18. 18.How many whole numbers lie between 30² and 31²?
  19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √6561? =
  22. 22.A square garden has an area of 81 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 361 square m. How long is each side (in m)?
  24. 24.What is 24²? =
  25. 25.What is 19²? =
  26. 26.How many whole numbers lie between 5² and 6²?
  27. 27.Which of these is a perfect square? (a) 1600 (b) 1671 (c) 1674
  28. 28.A square garden has an area of 1024 square m. How long is each side (in m)?
  29. 29.What is 17²? =
  30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  31. 31.Which of these is a perfect square? (a) 484 (b) 509 (c) 493
  32. 32.How many whole numbers lie between 6² and 7²?
  33. 33.What is 76²? =
  34. 34.What is 33²? =
  35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  36. 36.How many whole numbers lie between 42² and 43²?
  37. 37.A square garden has an area of 2601 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 289 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 15² and 16²?
  40. 40.A square garden has an area of 3481 square m. How long is each side (in m)?

Answer key

  1. 94
  2. 529
  3. 10
  4. 13
  5. 961
  6. 96
  7. 676
  8. 361
  9. 225
  10. 44
  11. 10
  12. 256
  13. 289
  14. 50
  15. 441
  16. 66
  17. 441
  18. 60
  19. 121
  20. 49
  21. 81
  22. 9
  23. 19
  24. 576
  25. 361
  26. 10
  27. 1600
  28. 32
  29. 289
  30. 529
  31. 484
  32. 12
  33. 5776
  34. 1089
  35. 841
  36. 84
  37. 51
  38. 17
  39. 30
  40. 59

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