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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 55 · 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 √961? =
  2. 2.What is √529? =
  3. 3.How many whole numbers lie between 50² and 51²?
  4. 4.What is 41²? =
  5. 5.What is 60²? =
  6. 6.What is 95²? =
  7. 7.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 344 (b) 324 (c) 348
  9. 9.What is the smallest whole number by which 343 must be divided to get a perfect square?
  10. 10.What is √6084? =
  11. 11.What is √1849? =
  12. 12.What is 32²? =
  13. 13.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 13²? =
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 58²? =
  18. 18.How many whole numbers lie between 33² and 34²?
  19. 19.How many whole numbers lie between 21² and 22²?
  20. 20.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  21. 21.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 320 must be divided to get a perfect square?
  24. 24.What is √3364? =
  25. 25.What is √121? =
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √9409? =
  28. 28.What is the smallest whole number by which 99 must be divided to get a perfect square?
  29. 29.A square garden has an area of 1089 square m. How long is each side (in m)?
  30. 30.What is √2704? =
  31. 31.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  32. 32.A square garden has an area of 841 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 529 square m. How long is each side (in m)?
  34. 34.What is √841? =
  35. 35.How many whole numbers lie between 6² and 7²?
  36. 36.What is 15²? =
  37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is 93²? =
  39. 39.What is √3136? =
  40. 40.What is √7569? =

Answer key

  1. 31
  2. 23
  3. 100
  4. 1681
  5. 3600
  6. 9025
  7. 5
  8. 324
  9. 7
  10. 78
  11. 43
  12. 1024
  13. 441
  14. 169
  15. 361
  16. 196
  17. 3364
  18. 66
  19. 42
  20. 3
  21. 2
  22. 36
  23. 5
  24. 58
  25. 11
  26. 841
  27. 97
  28. 11
  29. 33
  30. 52
  31. 256
  32. 29
  33. 23
  34. 29
  35. 12
  36. 225
  37. 576
  38. 8649
  39. 56
  40. 87

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