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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 246 · 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 19² and 20²?
  2. 2.A square garden has an area of 2916 square m. How long is each side (in m)?
  3. 3.What is 84²? =
  4. 4.What is 80²? =
  5. 5.How many whole numbers lie between 36² and 37²?
  6. 6.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  7. 7.How many whole numbers lie between 17² and 18²?
  8. 8.What is √2025? =
  9. 9.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 46²? =
  11. 11.A square garden has an area of 169 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 13² and 14²?
  13. 13.What is √6400? =
  14. 14.What is √7225? =
  15. 15.A square garden has an area of 3249 square m. How long is each side (in m)?
  16. 16.Which of these is a perfect square? (a) 484 (b) 513 (c) 522
  17. 17.A square garden has an area of 1849 square m. How long is each side (in m)?
  18. 18.A square garden has an area of 1296 square m. How long is each side (in m)?
  19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  20. 20.How many whole numbers lie between 41² and 42²?
  21. 21.How many whole numbers lie between 12² and 13²?
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 56²? =
  25. 25.What is √841? =
  26. 26.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 441 (b) 464 (c) 450
  28. 28.What is √529? =
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is 47²? =
  31. 31.What is 41²? =
  32. 32.How many whole numbers lie between 30² and 31²?
  33. 33.What is √676? =
  34. 34.Which of these is a perfect square? (a) 541 (b) 554 (c) 529
  35. 35.What is 16²? =
  36. 36.What is the smallest whole number by which 75 must be divided to get a perfect square?
  37. 37.How many whole numbers lie between 35² and 36²?
  38. 38.How many whole numbers lie between 22² and 23²?
  39. 39.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 637 must be divided to get a perfect square?

Answer key

  1. 38
  2. 54
  3. 7056
  4. 6400
  5. 72
  6. 13
  7. 34
  8. 45
  9. 484
  10. 2116
  11. 13
  12. 26
  13. 80
  14. 85
  15. 57
  16. 484
  17. 43
  18. 36
  19. 289
  20. 82
  21. 24
  22. 100
  23. 400
  24. 3136
  25. 29
  26. 10
  27. 441
  28. 23
  29. 256
  30. 2209
  31. 1681
  32. 60
  33. 26
  34. 529
  35. 256
  36. 3
  37. 70
  38. 44
  39. 13
  40. 13

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