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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 583 · 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 √625? =
  2. 2.What is 11²? =
  3. 3.A square garden has an area of 1849 square m. How long is each side (in m)?
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √729? =
  6. 6.Which of these is a perfect square? (a) 691 (b) 689 (c) 676
  7. 7.What is √841? =
  8. 8.What is √1296? =
  9. 9.What is 22²? =
  10. 10.How many whole numbers lie between 24² and 25²?
  11. 11.A square garden has an area of 2116 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 929 (b) 900 (c) 922
  13. 13.What is the smallest whole number by which 320 must be divided to get a perfect square?
  14. 14.What is √900? =
  15. 15.A square garden has an area of 576 square m. How long is each side (in m)?
  16. 16.What is 78²? =
  17. 17.A square garden has an area of 121 square m. How long is each side (in m)?
  18. 18.What is √576? =
  19. 19.How many whole numbers lie between 48² and 49²?
  20. 20.A square garden has an area of 3481 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 741 (b) 738 (c) 729
  22. 22.How many whole numbers lie between 25² and 26²?
  23. 23.A square garden has an area of 784 square m. How long is each side (in m)?
  24. 24.How many whole numbers lie between 12² and 13²?
  25. 25.What is √400? =
  26. 26.What is √3969? =
  27. 27.What is 43²? =
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √1024? =
  30. 30.What is 69²? =
  31. 31.What is √5184? =
  32. 32.What is 34²? =
  33. 33.Which of these is a perfect square? (a) 253 (b) 225 (c) 229
  34. 34.What is 81²? =
  35. 35.What is 90²? =
  36. 36.What is √361? =
  37. 37.What is 47²? =
  38. 38.Which of these is a perfect square? (a) 1480 (b) 1444 (c) 1476
  39. 39.What is √144? =
  40. 40.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 25
  2. 121
  3. 43
  4. 100
  5. 27
  6. 676
  7. 29
  8. 36
  9. 484
  10. 48
  11. 46
  12. 900
  13. 5
  14. 30
  15. 24
  16. 6084
  17. 11
  18. 24
  19. 96
  20. 59
  21. 729
  22. 50
  23. 28
  24. 24
  25. 20
  26. 63
  27. 1849
  28. 841
  29. 32
  30. 4761
  31. 72
  32. 1156
  33. 225
  34. 6561
  35. 8100
  36. 19
  37. 2209
  38. 1444
  39. 12
  40. 900

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