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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 162 · 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 19 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √3969? =
  3. 3.A square garden has an area of 676 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 17² and 18²?
  5. 5.Which of these is a perfect square? (a) 169 (b) 183 (c) 170
  6. 6.A square garden has an area of 1936 square m. How long is each side (in m)?
  7. 7.What is √961? =
  8. 8.What is 18²? =
  9. 9.Which of these is a perfect square? (a) 1445 (b) 1444 (c) 1471
  10. 10.What is 27²? =
  11. 11.What is √9801? =
  12. 12.How many whole numbers lie between 15² and 16²?
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 366 (b) 395 (c) 361
  15. 15.What is √2809? =
  16. 16.Which of these is a perfect square? (a) 1358 (b) 1340 (c) 1296
  17. 17.A square garden has an area of 1849 square m. How long is each side (in m)?
  18. 18.What is 60²? =
  19. 19.Which of these is a perfect square? (a) 900 (b) 957 (c) 943
  20. 20.Which of these is a perfect square? (a) 487 (b) 484 (c) 516
  21. 21.Which of these is a perfect square? (a) 311 (b) 289 (c) 312
  22. 22.How many whole numbers lie between 25² and 26²?
  23. 23.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 32² and 33²?
  25. 25.What is √1089? =
  26. 26.What is √5329? =
  27. 27.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √3364? =
  29. 29.How many whole numbers lie between 13² and 14²?
  30. 30.A square garden has an area of 729 square m. How long is each side (in m)?
  31. 31.What is 82²? =
  32. 32.A square garden has an area of 2601 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 41²? =
  36. 36.What is 84²? =
  37. 37.What is 43²? =
  38. 38.What is √676? =
  39. 39.What is 61²? =
  40. 40.What is the smallest whole number by which 27 must be multiplied to get a perfect square?

Answer key

  1. 361
  2. 63
  3. 26
  4. 34
  5. 169
  6. 44
  7. 31
  8. 324
  9. 1444
  10. 729
  11. 99
  12. 30
  13. 576
  14. 361
  15. 53
  16. 1296
  17. 43
  18. 3600
  19. 900
  20. 484
  21. 289
  22. 50
  23. 144
  24. 64
  25. 33
  26. 73
  27. 676
  28. 58
  29. 26
  30. 27
  31. 6724
  32. 51
  33. 784
  34. 841
  35. 1681
  36. 7056
  37. 1849
  38. 26
  39. 3721
  40. 3

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