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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 671 · 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 smallest whole number by which 80 must be multiplied to get a perfect square?
  2. 2.A square garden has an area of 3136 square m. How long is each side (in m)?
  3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  4. 4.Which of these is a perfect square? (a) 1497 (b) 1444 (c) 1479
  5. 5.A square garden has an area of 400 square m. How long is each side (in m)?
  6. 6.How many whole numbers lie between 7² and 8²?
  7. 7.What is 73²? =
  8. 8.How many whole numbers lie between 27² and 28²?
  9. 9.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 9² and 10²?
  11. 11.What is √8281? =
  12. 12.What is 55²? =
  13. 13.What is √121? =
  14. 14.How many whole numbers lie between 47² and 48²?
  15. 15.A square garden has an area of 841 square m. How long is each side (in m)?
  16. 16.What is 58²? =
  17. 17.What is 27²? =
  18. 18.A square garden has an area of 3025 square m. How long is each side (in m)?
  19. 19.What is 26²? =
  20. 20.Which of these is a perfect square? (a) 334 (b) 340 (c) 324
  21. 21.A square garden has an area of 2809 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 817 (b) 828 (c) 784
  23. 23.What is 86²? =
  24. 24.What is the smallest whole number by which 72 must be divided to get a perfect square?
  25. 25.What is the smallest whole number by which 405 must be divided to get a perfect square?
  26. 26.What is √400? =
  27. 27.What is 15²? =
  28. 28.A square garden has an area of 49 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 41² and 42²?
  30. 30.What is 62²? =
  31. 31.A square garden has an area of 2116 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 14² and 15²?
  35. 35.What is √529? =
  36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  37. 37.Which of these is a perfect square? (a) 846 (b) 841 (c) 884
  38. 38.A square garden has an area of 676 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 614 (b) 613 (c) 576
  40. 40.How many whole numbers lie between 17² and 18²?

Answer key

  1. 5
  2. 56
  3. 841
  4. 1444
  5. 20
  6. 14
  7. 5329
  8. 54
  9. 6
  10. 18
  11. 91
  12. 3025
  13. 11
  14. 94
  15. 29
  16. 3364
  17. 729
  18. 55
  19. 676
  20. 324
  21. 53
  22. 784
  23. 7396
  24. 2
  25. 5
  26. 20
  27. 225
  28. 7
  29. 82
  30. 3844
  31. 46
  32. 6
  33. 49
  34. 28
  35. 23
  36. 25
  37. 841
  38. 26
  39. 576
  40. 34

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