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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 216 · 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 sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  3. 3.What is 47²? =
  4. 4.Which of these is a perfect square? (a) 706 (b) 676 (c) 683
  5. 5.Which of these is a perfect square? (a) 101 (b) 109 (c) 100
  6. 6.How many whole numbers lie between 15² and 16²?
  7. 7.A square garden has an area of 100 square m. How long is each side (in m)?
  8. 8.What is √8100? =
  9. 9.What is √5625? =
  10. 10.What is √1225? =
  11. 11.What is 98²? =
  12. 12.A square garden has an area of 1024 square m. How long is each side (in m)?
  13. 13.What is √576? =
  14. 14.What is √8649? =
  15. 15.What is the smallest whole number by which 147 must be divided to get a perfect square?
  16. 16.A square garden has an area of 1089 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 1156 square m. How long is each side (in m)?
  18. 18.What is √144? =
  19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √4489? =
  21. 21.What is √1521? =
  22. 22.A square garden has an area of 1225 square m. How long is each side (in m)?
  23. 23.What is 62²? =
  24. 24.How many whole numbers lie between 10² and 11²?
  25. 25.How many whole numbers lie between 36² and 37²?
  26. 26.What is 51²? =
  27. 27.Which of these is a perfect square? (a) 1149 (b) 1140 (c) 1089
  28. 28.A square garden has an area of 1681 square m. How long is each side (in m)?
  29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 49 square m. How long is each side (in m)?
  31. 31.A square garden has an area of 64 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 284 (b) 256 (c) 267
  33. 33.A square garden has an area of 441 square m. How long is each side (in m)?
  34. 34.What is √2116? =
  35. 35.What is 35²? =
  36. 36.Which of these is a perfect square? (a) 470 (b) 450 (c) 441
  37. 37.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  38. 38.What is √900? =
  39. 39.A square garden has an area of 2601 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 47² and 48²?

Answer key

  1. 900
  2. 5
  3. 2209
  4. 676
  5. 100
  6. 30
  7. 10
  8. 90
  9. 75
  10. 35
  11. 9604
  12. 32
  13. 24
  14. 93
  15. 3
  16. 33
  17. 34
  18. 12
  19. 289
  20. 67
  21. 39
  22. 35
  23. 3844
  24. 20
  25. 72
  26. 2601
  27. 1089
  28. 41
  29. 121
  30. 7
  31. 8
  32. 256
  33. 21
  34. 46
  35. 1225
  36. 441
  37. 7
  38. 30
  39. 51
  40. 94

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