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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 520 · 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 √8100? =
  2. 2.What is √196? =
  3. 3.What is 28²? =
  4. 4.What is √2916? =
  5. 5.A square garden has an area of 400 square m. How long is each side (in m)?
  6. 6.How many whole numbers lie between 37² and 38²?
  7. 7.What is 26²? =
  8. 8.What is √5184? =
  9. 9.A square garden has an area of 2809 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 400 (b) 404 (c) 406
  11. 11.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  12. 12.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  13. 13.What is √121? =
  14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 468 must be divided to get a perfect square?
  16. 16.What is 54²? =
  17. 17.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √361? =
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  20. 20.How many whole numbers lie between 26² and 27²?
  21. 21.What is 74²? =
  22. 22.How many whole numbers lie between 38² and 39²?
  23. 23.How many whole numbers lie between 5² and 6²?
  24. 24.What is √7396? =
  25. 25.What is √7056? =
  26. 26.Which of these is a perfect square? (a) 509 (b) 488 (c) 484
  27. 27.Which of these is a perfect square? (a) 1387 (b) 1394 (c) 1369
  28. 28.How many whole numbers lie between 49² and 50²?
  29. 29.What is 50²? =
  30. 30.How many whole numbers lie between 10² and 11²?
  31. 31.What is √289? =
  32. 32.What is √1764? =
  33. 33.Which of these is a perfect square? (a) 367 (b) 361 (c) 389
  34. 34.A square garden has an area of 169 square m. How long is each side (in m)?
  35. 35.What is √6241? =
  36. 36.A square garden has an area of 1024 square m. How long is each side (in m)?
  37. 37.Which of these is a perfect square? (a) 141 (b) 143 (c) 121
  38. 38.What is 69²? =
  39. 39.A square garden has an area of 2500 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 759 (b) 729 (c) 758

Answer key

  1. 90
  2. 14
  3. 784
  4. 54
  5. 20
  6. 74
  7. 676
  8. 72
  9. 53
  10. 400
  11. 6
  12. 10
  13. 11
  14. 361
  15. 13
  16. 2916
  17. 900
  18. 19
  19. 484
  20. 52
  21. 5476
  22. 76
  23. 10
  24. 86
  25. 84
  26. 484
  27. 1369
  28. 98
  29. 2500
  30. 20
  31. 17
  32. 42
  33. 361
  34. 13
  35. 79
  36. 32
  37. 121
  38. 4761
  39. 50
  40. 729

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