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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 556 · 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.How many whole numbers lie between 10² and 11²?
  2. 2.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  3. 3.How many whole numbers lie between 43² and 44²?
  4. 4.A square garden has an area of 100 square m. How long is each side (in m)?
  5. 5.What is 86²? =
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √2704? =
  8. 8.What is 29²? =
  9. 9.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 1092 (b) 1155 (c) 1089
  12. 12.What is 65²? =
  13. 13.What is 54²? =
  14. 14.What is √961? =
  15. 15.How many whole numbers lie between 6² and 7²?
  16. 16.A square garden has an area of 729 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is 52²? =
  19. 19.A square garden has an area of 784 square m. How long is each side (in m)?
  20. 20.What is √225? =
  21. 21.A square garden has an area of 1521 square m. How long is each side (in m)?
  22. 22.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √1089? =
  24. 24.What is √7921? =
  25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  27. 27.A square garden has an area of 1156 square m. How long is each side (in m)?
  28. 28.What is 30²? =
  29. 29.What is √7569? =
  30. 30.How many whole numbers lie between 25² and 26²?
  31. 31.Which of these is a perfect square? (a) 256 (b) 264 (c) 270
  32. 32.A square garden has an area of 1444 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 2304 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 41² and 42²?
  35. 35.What is 27²? =
  36. 36.What is √3136? =
  37. 37.A square garden has an area of 169 square m. How long is each side (in m)?
  38. 38.What is √2209? =
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  40. 40.Which of these is a perfect square? (a) 961 (b) 966 (c) 990

Answer key

  1. 20
  2. 2
  3. 86
  4. 10
  5. 7396
  6. 81
  7. 52
  8. 841
  9. 5
  10. 729
  11. 1089
  12. 4225
  13. 2916
  14. 31
  15. 12
  16. 27
  17. 900
  18. 2704
  19. 28
  20. 15
  21. 39
  22. 196
  23. 33
  24. 89
  25. 361
  26. 2
  27. 34
  28. 900
  29. 87
  30. 50
  31. 256
  32. 38
  33. 48
  34. 82
  35. 729
  36. 56
  37. 13
  38. 47
  39. 100
  40. 961

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