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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 206 · 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.A square garden has an area of 441 square m. How long is each side (in m)?
  2. 2.How many whole numbers lie between 21² and 22²?
  3. 3.How many whole numbers lie between 6² and 7²?
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  5. 5.Which of these is a perfect square? (a) 841 (b) 887 (c) 850
  6. 6.What is √5776? =
  7. 7.What is 12²? =
  8. 8.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 40² and 41²?
  10. 10.A square garden has an area of 289 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 49 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 48² and 49²?
  13. 13.What is √8649? =
  14. 14.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 1020 (b) 1001 (c) 961
  16. 16.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  18. 18.A square garden has an area of 1369 square m. How long is each side (in m)?
  19. 19.What is 40²? =
  20. 20.What is 90²? =
  21. 21.What is 15²? =
  22. 22.Which of these is a perfect square? (a) 376 (b) 388 (c) 361
  23. 23.How many whole numbers lie between 12² and 13²?
  24. 24.What is √256? =
  25. 25.What is √7396? =
  26. 26.What is 18²? =
  27. 27.A square garden has an area of 3025 square m. How long is each side (in m)?
  28. 28.What is √7569? =
  29. 29.What is √1225? =
  30. 30.What is √1024? =
  31. 31.How many whole numbers lie between 32² and 33²?
  32. 32.What is the smallest whole number by which 135 must be divided to get a perfect square?
  33. 33.What is √5184? =
  34. 34.What is √6724? =
  35. 35.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  36. 36.What is √2304? =
  37. 37.What is 93²? =
  38. 38.How many whole numbers lie between 24² and 25²?
  39. 39.A square garden has an area of 729 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 201 (b) 196 (c) 224

Answer key

  1. 21
  2. 42
  3. 12
  4. 441
  5. 841
  6. 76
  7. 144
  8. 256
  9. 80
  10. 17
  11. 7
  12. 96
  13. 93
  14. 7
  15. 961
  16. 576
  17. 400
  18. 37
  19. 1600
  20. 8100
  21. 225
  22. 361
  23. 24
  24. 16
  25. 86
  26. 324
  27. 55
  28. 87
  29. 35
  30. 32
  31. 64
  32. 15
  33. 72
  34. 82
  35. 10
  36. 48
  37. 8649
  38. 48
  39. 27
  40. 196

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