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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 431 · 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) 1366 (b) 1307 (c) 1296
  2. 2.What is √5625? =
  3. 3.A square garden has an area of 3600 square m. How long is each side (in m)?
  4. 4.What is 39²? =
  5. 5.What is the smallest whole number by which 832 must be divided to get a perfect square?
  6. 6.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  7. 7.A square garden has an area of 2809 square m. How long is each side (in m)?
  8. 8.What is √5184? =
  9. 9.What is √6084? =
  10. 10.Which of these is a perfect square? (a) 144 (b) 163 (c) 154
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √9801? =
  13. 13.How many whole numbers lie between 48² and 49²?
  14. 14.Which of these is a perfect square? (a) 650 (b) 625 (c) 672
  15. 15.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  16. 16.A square garden has an area of 729 square m. How long is each side (in m)?
  17. 17.What is 92²? =
  18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 252 must be divided to get a perfect square?
  20. 20.What is 26²? =
  21. 21.What is 89²? =
  22. 22.A square garden has an area of 400 square m. How long is each side (in m)?
  23. 23.What is 25²? =
  24. 24.Which of these is a perfect square? (a) 1244 (b) 1225 (c) 1285
  25. 25.How many whole numbers lie between 43² and 44²?
  26. 26.What is the smallest whole number by which 44 must be divided to get a perfect square?
  27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  28. 28.Which of these is a perfect square? (a) 1024 (b) 1037 (c) 1038
  29. 29.A square garden has an area of 1444 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  31. 31.What is √1225? =
  32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  33. 33.Which of these is a perfect square? (a) 400 (b) 425 (c) 411
  34. 34.How many whole numbers lie between 14² and 15²?
  35. 35.How many whole numbers lie between 45² and 46²?
  36. 36.A square garden has an area of 324 square m. How long is each side (in m)?
  37. 37.What is the smallest whole number by which 45 must be divided to get a perfect square?
  38. 38.How many whole numbers lie between 10² and 11²?
  39. 39.A square garden has an area of 289 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 64 square m. How long is each side (in m)?

Answer key

  1. 1296
  2. 75
  3. 60
  4. 1521
  5. 13
  6. 784
  7. 53
  8. 72
  9. 78
  10. 144
  11. 484
  12. 99
  13. 96
  14. 625
  15. 15
  16. 27
  17. 8464
  18. 121
  19. 7
  20. 676
  21. 7921
  22. 20
  23. 625
  24. 1225
  25. 86
  26. 11
  27. 361
  28. 1024
  29. 38
  30. 6
  31. 35
  32. 144
  33. 400
  34. 28
  35. 90
  36. 18
  37. 5
  38. 20
  39. 17
  40. 8

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