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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 412 · 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 √5625? =
  2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is 75²? =
  4. 4.How many whole numbers lie between 18² and 19²?
  5. 5.What is 51²? =
  6. 6.How many whole numbers lie between 22² and 23²?
  7. 7.What is √9604? =
  8. 8.What is √1156? =
  9. 9.How many whole numbers lie between 12² and 13²?
  10. 10.How many whole numbers lie between 38² and 39²?
  11. 11.Which of these is a perfect square? (a) 823 (b) 784 (c) 811
  12. 12.Which of these is a perfect square? (a) 1117 (b) 1089 (c) 1140
  13. 13.How many whole numbers lie between 23² and 24²?
  14. 14.A square garden has an area of 2025 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 121 square m. How long is each side (in m)?
  16. 16.What is √1444? =
  17. 17.Which of these is a perfect square? (a) 233 (b) 225 (c) 230
  18. 18.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  19. 19.What is √1225? =
  20. 20.What is 58²? =
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  23. 23.A square garden has an area of 400 square m. How long is each side (in m)?
  24. 24.How many whole numbers lie between 41² and 42²?
  25. 25.What is 85²? =
  26. 26.What is √1764? =
  27. 27.What is √8836? =
  28. 28.How many whole numbers lie between 11² and 12²?
  29. 29.What is the smallest whole number by which 128 must be divided to get a perfect square?
  30. 30.How many whole numbers lie between 29² and 30²?
  31. 31.A square garden has an area of 49 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 24² and 25²?
  33. 33.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  35. 35.Which of these is a perfect square? (a) 127 (b) 128 (c) 121
  36. 36.How many whole numbers lie between 7² and 8²?
  37. 37.A square garden has an area of 3136 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 100 square m. How long is each side (in m)?
  39. 39.What is √2916? =
  40. 40.What is √841? =

Answer key

  1. 75
  2. 169
  3. 5625
  4. 36
  5. 2601
  6. 44
  7. 98
  8. 34
  9. 24
  10. 76
  11. 784
  12. 1089
  13. 46
  14. 45
  15. 11
  16. 38
  17. 225
  18. 14
  19. 35
  20. 3364
  21. 676
  22. 729
  23. 20
  24. 82
  25. 7225
  26. 42
  27. 94
  28. 22
  29. 2
  30. 58
  31. 7
  32. 48
  33. 900
  34. 256
  35. 121
  36. 14
  37. 56
  38. 10
  39. 54
  40. 29

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