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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 533 · 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 78²? =
  2. 2.What is 33²? =
  3. 3.What is 97²? =
  4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 289 square m. How long is each side (in m)?
  6. 6.How many whole numbers lie between 38² and 39²?
  7. 7.Which of these is a perfect square? (a) 900 (b) 953 (c) 909
  8. 8.What is 84²? =
  9. 9.What is 11²? =
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 1407 (b) 1402 (c) 1369
  12. 12.How many whole numbers lie between 15² and 16²?
  13. 13.What is 62²? =
  14. 14.Which of these is a perfect square? (a) 379 (b) 361 (c) 365
  15. 15.What is √2401? =
  16. 16.A square garden has an area of 400 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 14² and 15²?
  18. 18.What is 12²? =
  19. 19.A square garden has an area of 256 square m. How long is each side (in m)?
  20. 20.What is √484? =
  21. 21.What is √961? =
  22. 22.What is 32²? =
  23. 23.What is √289? =
  24. 24.How many whole numbers lie between 12² and 13²?
  25. 25.What is the smallest whole number by which 63 must be divided to get a perfect square?
  26. 26.Which of these is a perfect square? (a) 731 (b) 729 (c) 770
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √3844? =
  29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  30. 30.Which of these is a perfect square? (a) 961 (b) 994 (c) 986
  31. 31.What is √1764? =
  32. 32.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 19² and 20²?
  34. 34.What is 25²? =
  35. 35.What is √1444? =
  36. 36.What is √1521? =
  37. 37.A square garden has an area of 196 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 2116 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 897 (b) 841 (c) 877
  40. 40.Which of these is a perfect square? (a) 575 (b) 529 (c) 552

Answer key

  1. 6084
  2. 1089
  3. 9409
  4. 36
  5. 17
  6. 76
  7. 900
  8. 7056
  9. 121
  10. 49
  11. 1369
  12. 30
  13. 3844
  14. 361
  15. 49
  16. 20
  17. 28
  18. 144
  19. 16
  20. 22
  21. 31
  22. 1024
  23. 17
  24. 24
  25. 7
  26. 729
  27. 484
  28. 62
  29. 900
  30. 961
  31. 42
  32. 576
  33. 38
  34. 625
  35. 38
  36. 39
  37. 14
  38. 46
  39. 841
  40. 529

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