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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 591 · 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 √3364? =
  2. 2.A square garden has an area of 289 square m. How long is each side (in m)?
  3. 3.What is √3136? =
  4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 1089 square m. How long is each side (in m)?
  6. 6.What is 16²? =
  7. 7.A square garden has an area of 576 square m. How long is each side (in m)?
  8. 8.What is √9216? =
  9. 9.How many whole numbers lie between 25² and 26²?
  10. 10.What is √1936? =
  11. 11.A square garden has an area of 529 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 243 must be divided to get a perfect square?
  16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √5625? =
  18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 625 (b) 648 (c) 659
  20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 1043 (b) 1024 (c) 1046
  22. 22.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  23. 23.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √2704? =
  25. 25.Which of these is a perfect square? (a) 361 (b) 364 (c) 395
  26. 26.How many whole numbers lie between 41² and 42²?
  27. 27.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 73²? =
  29. 29.What is √3481? =
  30. 30.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 169 (b) 193 (c) 191
  32. 32.What is 24²? =
  33. 33.What is the smallest whole number by which 50 must be divided to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 573 (b) 529 (c) 560
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  36. 36.How many whole numbers lie between 7² and 8²?
  37. 37.Which of these is a perfect square? (a) 250 (b) 225 (c) 248
  38. 38.Which of these is a perfect square? (a) 759 (b) 755 (c) 729
  39. 39.Which of these is a perfect square? (a) 961 (b) 989 (c) 974
  40. 40.Which of these is a perfect square? (a) 1562 (b) 1523 (c) 1521

Answer key

  1. 58
  2. 17
  3. 56
  4. 324
  5. 33
  6. 256
  7. 24
  8. 96
  9. 50
  10. 44
  11. 23
  12. 289
  13. 100
  14. 529
  15. 3
  16. 169
  17. 75
  18. 400
  19. 625
  20. 441
  21. 1024
  22. 14
  23. 484
  24. 52
  25. 361
  26. 82
  27. 576
  28. 5329
  29. 59
  30. 5
  31. 169
  32. 576
  33. 2
  34. 529
  35. 625
  36. 14
  37. 225
  38. 729
  39. 961
  40. 1521

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