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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 731 · 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 √6400? =
  2. 2.What is the smallest whole number by which 832 must be divided to get a perfect square?
  3. 3.What is 46²? =
  4. 4.Which of these is a perfect square? (a) 159 (b) 158 (c) 144
  5. 5.What is 91²? =
  6. 6.What is √729? =
  7. 7.What is 79²? =
  8. 8.A square garden has an area of 1764 square m. How long is each side (in m)?
  9. 9.What is 12²? =
  10. 10.What is √7225? =
  11. 11.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  12. 12.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  13. 13.What is √6724? =
  14. 14.How many whole numbers lie between 8² and 9²?
  15. 15.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 29²? =
  17. 17.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  18. 18.Which of these is a perfect square? (a) 529 (b) 557 (c) 541
  19. 19.What is √529? =
  20. 20.What is √484? =
  21. 21.Which of these is a perfect square? (a) 324 (b) 330 (c) 328
  22. 22.What is √144? =
  23. 23.What is the smallest whole number by which 128 must be divided to get a perfect square?
  24. 24.What is 13²? =
  25. 25.What is √1849? =
  26. 26.What is √3364? =
  27. 27.How many whole numbers lie between 36² and 37²?
  28. 28.What is √1681? =
  29. 29.What is 95²? =
  30. 30.What is √4225? =
  31. 31.What is the smallest whole number by which 99 must be divided to get a perfect square?
  32. 32.What is 11²? =
  33. 33.What is √225? =
  34. 34.What is 63²? =
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  36. 36.How many whole numbers lie between 44² and 45²?
  37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is 53²? =
  39. 39.What is √3721? =
  40. 40.What is √1369? =

Answer key

  1. 80
  2. 13
  3. 2116
  4. 144
  5. 8281
  6. 27
  7. 6241
  8. 42
  9. 144
  10. 85
  11. 11
  12. 14
  13. 82
  14. 16
  15. 121
  16. 841
  17. 256
  18. 529
  19. 23
  20. 22
  21. 324
  22. 12
  23. 2
  24. 169
  25. 43
  26. 58
  27. 72
  28. 41
  29. 9025
  30. 65
  31. 11
  32. 121
  33. 15
  34. 3969
  35. 289
  36. 88
  37. 484
  38. 2809
  39. 61
  40. 37

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