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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 288 · 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.How many whole numbers lie between 35² and 36²?
  2. 2.What is 64²? =
  3. 3.Which of these is a perfect square? (a) 361 (b) 399 (c) 374
  4. 4.A square garden has an area of 49 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 28 must be divided to get a perfect square?
  6. 6.What is 50²? =
  7. 7.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  8. 8.What is 19²? =
  9. 9.What is 12²? =
  10. 10.How many whole numbers lie between 24² and 25²?
  11. 11.How many whole numbers lie between 7² and 8²?
  12. 12.A square garden has an area of 81 square m. How long is each side (in m)?
  13. 13.What is √169? =
  14. 14.A square garden has an area of 1600 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 20 must be divided to get a perfect square?
  16. 16.A square garden has an area of 121 square m. How long is each side (in m)?
  17. 17.What is 35²? =
  18. 18.Which of these is a perfect square? (a) 460 (b) 441 (c) 470
  19. 19.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 3481 square m. How long is each side (in m)?
  21. 21.What is √5929? =
  22. 22.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 42² and 43²?
  24. 24.What is the smallest whole number by which 504 must be divided to get a perfect square?
  25. 25.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 63²? =
  27. 27.What is √7396? =
  28. 28.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the smallest whole number by which 96 must be divided to get a perfect square?
  30. 30.What is √256? =
  31. 31.Which of these is a perfect square? (a) 1063 (b) 1024 (c) 1051
  32. 32.Which of these is a perfect square? (a) 828 (b) 824 (c) 784
  33. 33.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  34. 34.A square garden has an area of 324 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 43² and 44²?
  36. 36.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  37. 37.A square garden has an area of 225 square m. How long is each side (in m)?
  38. 38.What is √324? =
  39. 39.What is √6400? =
  40. 40.What is 42²? =

Answer key

  1. 70
  2. 4096
  3. 361
  4. 7
  5. 7
  6. 2500
  7. 6
  8. 361
  9. 144
  10. 48
  11. 14
  12. 9
  13. 13
  14. 40
  15. 5
  16. 11
  17. 1225
  18. 441
  19. 15
  20. 59
  21. 77
  22. 256
  23. 84
  24. 14
  25. 81
  26. 3969
  27. 86
  28. 289
  29. 6
  30. 16
  31. 1024
  32. 784
  33. 5
  34. 18
  35. 86
  36. 7
  37. 15
  38. 18
  39. 80
  40. 1764

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