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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 447 · 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 √2209? =
  2. 2.What is 82²? =
  3. 3.How many whole numbers lie between 9² and 10²?
  4. 4.What is √3249? =
  5. 5.What is √6889? =
  6. 6.How many whole numbers lie between 43² and 44²?
  7. 7.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  8. 8.How many whole numbers lie between 26² and 27²?
  9. 9.A square garden has an area of 25 square m. How long is each side (in m)?
  10. 10.How many whole numbers lie between 44² and 45²?
  11. 11.What is 37²? =
  12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 1444 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 390 (b) 372 (c) 361
  15. 15.What is 91²? =
  16. 16.What is √6084? =
  17. 17.Which of these is a perfect square? (a) 251 (b) 249 (c) 225
  18. 18.Which of these is a perfect square? (a) 278 (b) 288 (c) 256
  19. 19.What is 61²? =
  20. 20.What is 40²? =
  21. 21.What is 33²? =
  22. 22.What is √2116? =
  23. 23.What is √676? =
  24. 24.What is √4225? =
  25. 25.What is 96²? =
  26. 26.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  27. 27.What is √529? =
  28. 28.Which of these is a perfect square? (a) 1089 (b) 1099 (c) 1097
  29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 27² and 28²?
  31. 31.What is √1369? =
  32. 32.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  33. 33.What is 13²? =
  34. 34.How many whole numbers lie between 23² and 24²?
  35. 35.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  36. 36.How many whole numbers lie between 48² and 49²?
  37. 37.What is 63²? =
  38. 38.A square garden has an area of 3364 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 6² and 7²?
  40. 40.What is 14²? =

Answer key

  1. 47
  2. 6724
  3. 18
  4. 57
  5. 83
  6. 86
  7. 5
  8. 52
  9. 5
  10. 88
  11. 1369
  12. 289
  13. 38
  14. 361
  15. 8281
  16. 78
  17. 225
  18. 256
  19. 3721
  20. 1600
  21. 1089
  22. 46
  23. 26
  24. 65
  25. 9216
  26. 11
  27. 23
  28. 1089
  29. 400
  30. 54
  31. 37
  32. 6
  33. 169
  34. 46
  35. 6
  36. 96
  37. 3969
  38. 58
  39. 12
  40. 196

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