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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 646 · 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.Which of these is a perfect square? (a) 1100 (b) 1124 (c) 1089
  2. 2.Which of these is a perfect square? (a) 385 (b) 361 (c) 391
  3. 3.How many whole numbers lie between 36² and 37²?
  4. 4.How many whole numbers lie between 44² and 45²?
  5. 5.How many whole numbers lie between 15² and 16²?
  6. 6.What is 35²? =
  7. 7.How many whole numbers lie between 28² and 29²?
  8. 8.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 85²? =
  10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 667 (b) 625 (c) 652
  12. 12.What is √9025? =
  13. 13.What is √6400? =
  14. 14.What is √4761? =
  15. 15.What is 74²? =
  16. 16.What is 51²? =
  17. 17.What is √900? =
  18. 18.What is 90²? =
  19. 19.What is √6724? =
  20. 20.What is 18²? =
  21. 21.A square garden has an area of 324 square m. How long is each side (in m)?
  22. 22.What is 62²? =
  23. 23.A square garden has an area of 400 square m. How long is each side (in m)?
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  25. 25.A square garden has an area of 441 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 1024 (b) 1038 (c) 1054
  27. 27.Which of these is a perfect square? (a) 184 (b) 169 (c) 192
  28. 28.A square garden has an area of 676 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 2209 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 1521 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 539 must be divided to get a perfect square?
  32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 41² and 42²?
  34. 34.What is 92²? =
  35. 35.What is 14²? =
  36. 36.What is √3249? =
  37. 37.A square garden has an area of 121 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 8² and 9²?
  39. 39.What is the smallest whole number by which 704 must be divided to get a perfect square?
  40. 40.How many whole numbers lie between 27² and 28²?

Answer key

  1. 1089
  2. 361
  3. 72
  4. 88
  5. 30
  6. 1225
  7. 56
  8. 121
  9. 7225
  10. 25
  11. 625
  12. 95
  13. 80
  14. 69
  15. 5476
  16. 2601
  17. 30
  18. 8100
  19. 82
  20. 324
  21. 18
  22. 3844
  23. 20
  24. 256
  25. 21
  26. 1024
  27. 169
  28. 26
  29. 47
  30. 39
  31. 11
  32. 144
  33. 82
  34. 8464
  35. 196
  36. 57
  37. 11
  38. 16
  39. 11
  40. 54

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