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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 704 · 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 1225 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 261 (b) 256 (c) 264
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 41² and 42²?
  5. 5.What is the smallest whole number by which 216 must be divided to get a perfect square?
  6. 6.How many whole numbers lie between 12² and 13²?
  7. 7.What is 21²? =
  8. 8.A square garden has an area of 2500 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 832 must be divided to get a perfect square?
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is √4900? =
  12. 12.What is the sum of the first 23 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.Which of these is a perfect square? (a) 1233 (b) 1225 (c) 1253
  15. 15.A square garden has an area of 1444 square m. How long is each side (in m)?
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 51²? =
  18. 18.What is the smallest whole number by which 32 must be divided to get a perfect square?
  19. 19.What is 39²? =
  20. 20.What is the smallest whole number by which 175 must be divided to get a perfect square?
  21. 21.A square garden has an area of 1681 square m. How long is each side (in m)?
  22. 22.How many whole numbers lie between 32² and 33²?
  23. 23.What is √529? =
  24. 24.What is 41²? =
  25. 25.What is 22²? =
  26. 26.How many whole numbers lie between 26² and 27²?
  27. 27.What is 42²? =
  28. 28.What is √2304? =
  29. 29.A square garden has an area of 36 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 196 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  32. 32.What is √9216? =
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 87²? =
  35. 35.How many whole numbers lie between 15² and 16²?
  36. 36.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  37. 37.What is √7396? =
  38. 38.What is the smallest whole number by which 243 must be divided to get a perfect square?
  39. 39.What is 40²? =
  40. 40.What is the smallest whole number by which 63 must be divided to get a perfect square?

Answer key

  1. 35
  2. 256
  3. 36
  4. 82
  5. 6
  6. 24
  7. 441
  8. 50
  9. 13
  10. 81
  11. 70
  12. 529
  13. 5
  14. 1225
  15. 38
  16. 900
  17. 2601
  18. 2
  19. 1521
  20. 7
  21. 41
  22. 64
  23. 23
  24. 1681
  25. 484
  26. 52
  27. 1764
  28. 48
  29. 6
  30. 14
  31. 6
  32. 96
  33. 361
  34. 7569
  35. 30
  36. 5
  37. 86
  38. 3
  39. 1600
  40. 7

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