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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 345 · 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 √484? =
  2. 2.Which of these is a perfect square? (a) 961 (b) 1007 (c) 987
  3. 3.A square garden has an area of 2916 square m. How long is each side (in m)?
  4. 4.What is 40²? =
  5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 43² and 44²?
  8. 8.How many whole numbers lie between 41² and 42²?
  9. 9.What is 65²? =
  10. 10.What is 73²? =
  11. 11.A square garden has an area of 400 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 583 (b) 594 (c) 576
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 50²? =
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  16. 16.How many whole numbers lie between 7² and 8²?
  17. 17.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √784? =
  19. 19.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  20. 20.What is √1936? =
  21. 21.What is 37²? =
  22. 22.How many whole numbers lie between 14² and 15²?
  23. 23.What is √900? =
  24. 24.How many whole numbers lie between 40² and 41²?
  25. 25.What is 72²? =
  26. 26.Which of these is a perfect square? (a) 163 (b) 144 (c) 150
  27. 27.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √2809? =
  29. 29.What is the smallest whole number by which 28 must be divided to get a perfect square?
  30. 30.A square garden has an area of 2304 square m. How long is each side (in m)?
  31. 31.A square garden has an area of 1936 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 31² and 32²?
  33. 33.What is √5929? =
  34. 34.What is 22²? =
  35. 35.What is the smallest whole number by which 243 must be divided to get a perfect square?
  36. 36.How many whole numbers lie between 20² and 21²?
  37. 37.Which of these is a perfect square? (a) 329 (b) 354 (c) 324
  38. 38.A square garden has an area of 961 square m. How long is each side (in m)?
  39. 39.What is 57²? =
  40. 40.What is √7921? =

Answer key

  1. 22
  2. 961
  3. 54
  4. 1600
  5. 121
  6. 900
  7. 86
  8. 82
  9. 4225
  10. 5329
  11. 20
  12. 576
  13. 841
  14. 2500
  15. 100
  16. 14
  17. 400
  18. 28
  19. 7
  20. 44
  21. 1369
  22. 28
  23. 30
  24. 80
  25. 5184
  26. 144
  27. 225
  28. 53
  29. 7
  30. 48
  31. 44
  32. 62
  33. 77
  34. 484
  35. 3
  36. 40
  37. 324
  38. 31
  39. 3249
  40. 89

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