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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 346 · 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.Which of these is a perfect square? (a) 1546 (b) 1521 (c) 1526
  2. 2.What is 71²? =
  3. 3.What is 13²? =
  4. 4.What is 16²? =
  5. 5.What is the smallest whole number by which 72 must be divided to get a perfect square?
  6. 6.What is √2025? =
  7. 7.What is 65²? =
  8. 8.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  9. 9.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 49²? =
  11. 11.Which of these is a perfect square? (a) 841 (b) 894 (c) 846
  12. 12.Which of these is a perfect square? (a) 1417 (b) 1439 (c) 1369
  13. 13.Which of these is a perfect square? (a) 120 (b) 102 (c) 100
  14. 14.What is √3721? =
  15. 15.How many whole numbers lie between 26² and 27²?
  16. 16.How many whole numbers lie between 25² and 26²?
  17. 17.Which of these is a perfect square? (a) 146 (b) 159 (c) 144
  18. 18.How many whole numbers lie between 44² and 45²?
  19. 19.A square garden has an area of 1936 square m. How long is each side (in m)?
  20. 20.What is √4624? =
  21. 21.A square garden has an area of 1849 square m. How long is each side (in m)?
  22. 22.What is √6724? =
  23. 23.What is √1849? =
  24. 24.What is √2916? =
  25. 25.A square garden has an area of 676 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 50 must be divided to get a perfect square?
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 3249 square m. How long is each side (in m)?
  29. 29.What is 58²? =
  30. 30.What is 64²? =
  31. 31.Which of these is a perfect square? (a) 1223 (b) 1163 (c) 1156
  32. 32.How many whole numbers lie between 12² and 13²?
  33. 33.What is √400? =
  34. 34.How many whole numbers lie between 7² and 8²?
  35. 35.A square garden has an area of 225 square m. How long is each side (in m)?
  36. 36.What is √1369? =
  37. 37.A square garden has an area of 3600 square m. How long is each side (in m)?
  38. 38.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 284 (b) 256 (c) 288
  40. 40.What is √256? =

Answer key

  1. 1521
  2. 5041
  3. 169
  4. 256
  5. 2
  6. 45
  7. 4225
  8. 14
  9. 324
  10. 2401
  11. 841
  12. 1369
  13. 100
  14. 61
  15. 52
  16. 50
  17. 144
  18. 88
  19. 44
  20. 68
  21. 43
  22. 82
  23. 43
  24. 54
  25. 26
  26. 2
  27. 49
  28. 57
  29. 3364
  30. 4096
  31. 1156
  32. 24
  33. 20
  34. 14
  35. 15
  36. 37
  37. 60
  38. 484
  39. 256
  40. 16

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