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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 348 · 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 the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 35² and 36²?
  4. 4.What is 84²? =
  5. 5.What is 47²? =
  6. 6.What is the smallest whole number by which 405 must be divided to get a perfect square?
  7. 7.What is √5776? =
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 484 square m. How long is each side (in m)?
  10. 10.How many whole numbers lie between 32² and 33²?
  11. 11.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 625 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 55²? =
  15. 15.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 22²? =
  17. 17.What is 76²? =
  18. 18.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  19. 19.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  20. 20.How many whole numbers lie between 25² and 26²?
  21. 21.Which of these is a perfect square? (a) 1597 (b) 1521 (c) 1580
  22. 22.How many whole numbers lie between 14² and 15²?
  23. 23.How many whole numbers lie between 26² and 27²?
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  26. 26.How many whole numbers lie between 34² and 35²?
  27. 27.A square garden has an area of 1024 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 100 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 75 must be divided to get a perfect square?
  30. 30.How many whole numbers lie between 9² and 10²?
  31. 31.How many whole numbers lie between 10² and 11²?
  32. 32.What is 59²? =
  33. 33.A square garden has an area of 961 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 8² and 9²?
  35. 35.How many whole numbers lie between 21² and 22²?
  36. 36.What is √6084? =
  37. 37.What is 26²? =
  38. 38.Which of these is a perfect square? (a) 100 (b) 115 (c) 103
  39. 39.What is 34²? =
  40. 40.What is √1444? =

Answer key

  1. 576
  2. 625
  3. 70
  4. 7056
  5. 2209
  6. 5
  7. 76
  8. 100
  9. 22
  10. 64
  11. 441
  12. 25
  13. 400
  14. 3025
  15. 289
  16. 484
  17. 5776
  18. 14
  19. 3
  20. 50
  21. 1521
  22. 28
  23. 52
  24. 144
  25. 121
  26. 68
  27. 32
  28. 10
  29. 3
  30. 18
  31. 20
  32. 3481
  33. 31
  34. 16
  35. 42
  36. 78
  37. 676
  38. 100
  39. 1156
  40. 38

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