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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 57 · 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 √625? =
  2. 2.A square garden has an area of 625 square m. How long is each side (in m)?
  3. 3.How many whole numbers lie between 16² and 17²?
  4. 4.What is √4489? =
  5. 5.How many whole numbers lie between 48² and 49²?
  6. 6.What is √729? =
  7. 7.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 224 (b) 203 (c) 196
  9. 9.A square garden has an area of 441 square m. How long is each side (in m)?
  10. 10.What is 84²? =
  11. 11.What is 22²? =
  12. 12.What is 70²? =
  13. 13.What is √324? =
  14. 14.How many whole numbers lie between 15² and 16²?
  15. 15.Which of these is a perfect square? (a) 121 (b) 127 (c) 136
  16. 16.What is 23²? =
  17. 17.How many whole numbers lie between 13² and 14²?
  18. 18.What is √2500? =
  19. 19.A square garden has an area of 3481 square m. How long is each side (in m)?
  20. 20.What is √3844? =
  21. 21.How many whole numbers lie between 41² and 42²?
  22. 22.What is the smallest whole number by which 99 must be divided to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 256 (b) 257 (c) 264
  24. 24.Which of these is a perfect square? (a) 327 (b) 331 (c) 324
  25. 25.What is 92²? =
  26. 26.What is √9801? =
  27. 27.A square garden has an area of 3025 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 49² and 50²?
  29. 29.What is √6084? =
  30. 30.How many whole numbers lie between 38² and 39²?
  31. 31.What is √9025? =
  32. 32.How many whole numbers lie between 22² and 23²?
  33. 33.What is the smallest whole number by which 250 must be divided to get a perfect square?
  34. 34.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 2116 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is √1225? =
  38. 38.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  40. 40.Which of these is a perfect square? (a) 1296 (b) 1326 (c) 1364

Answer key

  1. 25
  2. 25
  3. 32
  4. 67
  5. 96
  6. 27
  7. 6
  8. 196
  9. 21
  10. 7056
  11. 484
  12. 4900
  13. 18
  14. 30
  15. 121
  16. 529
  17. 26
  18. 50
  19. 59
  20. 62
  21. 82
  22. 11
  23. 256
  24. 324
  25. 8464
  26. 99
  27. 55
  28. 98
  29. 78
  30. 76
  31. 95
  32. 44
  33. 10
  34. 324
  35. 46
  36. 25
  37. 35
  38. 100
  39. 361
  40. 1296

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