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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 651 · 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 25 odd numbers (1 + 3 + 5 + …)?
  2. 2.A square garden has an area of 289 square m. How long is each side (in m)?
  3. 3.What is 55²? =
  4. 4.What is √2116? =
  5. 5.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 100 (b) 106 (c) 120
  7. 7.What is 36²? =
  8. 8.What is √3844? =
  9. 9.What is √6889? =
  10. 10.Which of these is a perfect square? (a) 383 (b) 361 (c) 381
  11. 11.Which of these is a perfect square? (a) 130 (b) 125 (c) 121
  12. 12.What is the smallest whole number by which 8 must be divided to get a perfect square?
  13. 13.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  14. 14.What is √6400? =
  15. 15.A square garden has an area of 1444 square m. How long is each side (in m)?
  16. 16.What is 75²? =
  17. 17.What is √196? =
  18. 18.Which of these is a perfect square? (a) 567 (b) 541 (c) 529
  19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √4489? =
  21. 21.What is the smallest whole number by which 50 must be divided to get a perfect square?
  22. 22.A square garden has an area of 2209 square m. How long is each side (in m)?
  23. 23.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  24. 24.How many whole numbers lie between 11² and 12²?
  25. 25.Which of these is a perfect square? (a) 425 (b) 412 (c) 400
  26. 26.What is 84²? =
  27. 27.Which of these is a perfect square? (a) 484 (b) 511 (c) 506
  28. 28.What is the smallest whole number by which 56 must be divided to get a perfect square?
  29. 29.A square garden has an area of 256 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √6561? =
  32. 32.A square garden has an area of 2704 square m. How long is each side (in m)?
  33. 33.What is 24²? =
  34. 34.A square garden has an area of 1600 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 31² and 32²?
  36. 36.How many whole numbers lie between 41² and 42²?
  37. 37.What is √1089? =
  38. 38.How many whole numbers lie between 8² and 9²?
  39. 39.How many whole numbers lie between 33² and 34²?
  40. 40.What is 76²? =

Answer key

  1. 625
  2. 17
  3. 3025
  4. 46
  5. 2
  6. 100
  7. 1296
  8. 62
  9. 83
  10. 361
  11. 121
  12. 2
  13. 14
  14. 80
  15. 38
  16. 5625
  17. 14
  18. 529
  19. 100
  20. 67
  21. 2
  22. 47
  23. 6
  24. 22
  25. 400
  26. 7056
  27. 484
  28. 14
  29. 16
  30. 900
  31. 81
  32. 52
  33. 576
  34. 40
  35. 62
  36. 82
  37. 33
  38. 16
  39. 66
  40. 5776

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