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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 66 · 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 8 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √729? =
  3. 3.What is 86²? =
  4. 4.How many whole numbers lie between 13² and 14²?
  5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 729 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 2116 square m. How long is each side (in m)?
  8. 8.What is 64²? =
  9. 9.Which of these is a perfect square? (a) 704 (b) 676 (c) 711
  10. 10.A square garden has an area of 1296 square m. How long is each side (in m)?
  11. 11.How many whole numbers lie between 39² and 40²?
  12. 12.How many whole numbers lie between 41² and 42²?
  13. 13.What is the smallest whole number by which 896 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 1119 (b) 1089 (c) 1127
  15. 15.What is the smallest whole number by which 147 must be divided to get a perfect square?
  16. 16.A square garden has an area of 2809 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 36² and 37²?
  18. 18.What is √2209? =
  19. 19.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 1369 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 24² and 25²?
  22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  23. 23.A square garden has an area of 1849 square m. How long is each side (in m)?
  24. 24.What is √8649? =
  25. 25.What is 68²? =
  26. 26.Which of these is a perfect square? (a) 1225 (b) 1243 (c) 1260
  27. 27.Which of these is a perfect square? (a) 542 (b) 537 (c) 529
  28. 28.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  29. 29.What is √1444? =
  30. 30.What is 90²? =
  31. 31.What is √6084? =
  32. 32.Which of these is a perfect square? (a) 225 (b) 250 (c) 227
  33. 33.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 13²? =
  35. 35.A square garden has an area of 256 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 34² and 35²?
  37. 37.A square garden has an area of 81 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 2209 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 576 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 213 (b) 219 (c) 196

Answer key

  1. 64
  2. 27
  3. 7396
  4. 26
  5. 784
  6. 27
  7. 46
  8. 4096
  9. 676
  10. 36
  11. 78
  12. 82
  13. 14
  14. 1089
  15. 3
  16. 53
  17. 72
  18. 47
  19. 11
  20. 37
  21. 48
  22. 49
  23. 43
  24. 93
  25. 4624
  26. 1225
  27. 529
  28. 13
  29. 38
  30. 8100
  31. 78
  32. 225
  33. 100
  34. 169
  35. 16
  36. 68
  37. 9
  38. 47
  39. 24
  40. 196

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