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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 640 · 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 the smallest whole number by which 360 must be divided to get a perfect square?
  2. 2.What is 92²? =
  3. 3.What is √8836? =
  4. 4.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 2209 square m. How long is each side (in m)?
  7. 7.Which of these is a perfect square? (a) 218 (b) 204 (c) 196
  8. 8.What is 27²? =
  9. 9.How many whole numbers lie between 35² and 36²?
  10. 10.How many whole numbers lie between 11² and 12²?
  11. 11.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 25 square m. How long is each side (in m)?
  14. 14.How many whole numbers lie between 49² and 50²?
  15. 15.A square garden has an area of 36 square m. How long is each side (in m)?
  16. 16.What is √7569? =
  17. 17.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  18. 18.What is 34²? =
  19. 19.Which of these is a perfect square? (a) 452 (b) 442 (c) 441
  20. 20.What is 55²? =
  21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 32²? =
  23. 23.How many whole numbers lie between 24² and 25²?
  24. 24.What is 31²? =
  25. 25.Which of these is a perfect square? (a) 402 (b) 434 (c) 400
  26. 26.What is 16²? =
  27. 27.A square garden has an area of 2500 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  29. 29.Which of these is a perfect square? (a) 145 (b) 144 (c) 150
  30. 30.What is 49²? =
  31. 31.Which of these is a perfect square? (a) 181 (b) 171 (c) 169
  32. 32.What is 42²? =
  33. 33.What is √7744? =
  34. 34.Which of these is a perfect square? (a) 338 (b) 348 (c) 324
  35. 35.What is √4761? =
  36. 36.A square garden has an area of 1089 square m. How long is each side (in m)?
  37. 37.What is √225? =
  38. 38.How many whole numbers lie between 37² and 38²?
  39. 39.What is the smallest whole number by which 175 must be divided to get a perfect square?
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 10
  2. 8464
  3. 94
  4. 5
  5. 100
  6. 47
  7. 196
  8. 729
  9. 70
  10. 22
  11. 225
  12. 729
  13. 5
  14. 98
  15. 6
  16. 87
  17. 13
  18. 1156
  19. 441
  20. 3025
  21. 196
  22. 1024
  23. 48
  24. 961
  25. 400
  26. 256
  27. 50
  28. 81
  29. 144
  30. 2401
  31. 169
  32. 1764
  33. 88
  34. 324
  35. 69
  36. 33
  37. 15
  38. 74
  39. 7
  40. 36

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