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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 181 · 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 √2304? =
  2. 2.What is √4225? =
  3. 3.A square garden has an area of 1521 square m. How long is each side (in m)?
  4. 4.What is √1936? =
  5. 5.How many whole numbers lie between 10² and 11²?
  6. 6.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 900 (b) 947 (c) 908
  8. 8.How many whole numbers lie between 25² and 26²?
  9. 9.Which of these is a perfect square? (a) 256 (b) 264 (c) 281
  10. 10.How many whole numbers lie between 21² and 22²?
  11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 39²? =
  13. 13.Which of these is a perfect square? (a) 1000 (b) 1019 (c) 961
  14. 14.A square garden has an area of 961 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 2809 square m. How long is each side (in m)?
  16. 16.What is √3364? =
  17. 17.A square garden has an area of 3025 square m. How long is each side (in m)?
  18. 18.What is 74²? =
  19. 19.Which of these is a perfect square? (a) 144 (b) 167 (c) 159
  20. 20.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 1024 square m. How long is each side (in m)?
  22. 22.How many whole numbers lie between 45² and 46²?
  23. 23.What is 98²? =
  24. 24.Which of these is a perfect square? (a) 482 (b) 441 (c) 447
  25. 25.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  26. 26.A square garden has an area of 2304 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 14² and 15²?
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  29. 29.How many whole numbers lie between 7² and 8²?
  30. 30.How many whole numbers lie between 29² and 30²?
  31. 31.How many whole numbers lie between 34² and 35²?
  32. 32.A square garden has an area of 1681 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 3364 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  35. 35.Which of these is a perfect square? (a) 1093 (b) 1089 (c) 1136
  36. 36.What is 26²? =
  37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  38. 38.Which of these is a perfect square? (a) 563 (b) 529 (c) 551
  39. 39.A square garden has an area of 1089 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 48² and 49²?

Answer key

  1. 48
  2. 65
  3. 39
  4. 44
  5. 20
  6. 5
  7. 900
  8. 50
  9. 256
  10. 42
  11. 256
  12. 1521
  13. 961
  14. 31
  15. 53
  16. 58
  17. 55
  18. 5476
  19. 144
  20. 14
  21. 32
  22. 90
  23. 9604
  24. 441
  25. 11
  26. 48
  27. 28
  28. 841
  29. 14
  30. 58
  31. 68
  32. 41
  33. 58
  34. 25
  35. 1089
  36. 676
  37. 64
  38. 529
  39. 33
  40. 96

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