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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 678 · 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 √6724? =
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 784 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 38² and 39²?
  5. 5.What is 38²? =
  6. 6.How many whole numbers lie between 27² and 28²?
  7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 268 (b) 258 (c) 256
  10. 10.What is √5041? =
  11. 11.A square garden has an area of 1225 square m. How long is each side (in m)?
  12. 12.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  13. 13.How many whole numbers lie between 7² and 8²?
  14. 14.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 1542 (b) 1599 (c) 1521
  16. 16.What is √2401? =
  17. 17.Which of these is a perfect square? (a) 430 (b) 400 (c) 415
  18. 18.How many whole numbers lie between 5² and 6²?
  19. 19.Which of these is a perfect square? (a) 225 (b) 230 (c) 229
  20. 20.How many whole numbers lie between 49² and 50²?
  21. 21.What is the smallest whole number by which 735 must be divided to get a perfect square?
  22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  24. 24.How many whole numbers lie between 23² and 24²?
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √9025? =
  27. 27.What is √1764? =
  28. 28.Which of these is a perfect square? (a) 317 (b) 302 (c) 289
  29. 29.A square garden has an area of 2809 square m. How long is each side (in m)?
  30. 30.What is √961? =
  31. 31.How many whole numbers lie between 35² and 36²?
  32. 32.What is √4900? =
  33. 33.What is √121? =
  34. 34.Which of these is a perfect square? (a) 1125 (b) 1089 (c) 1139
  35. 35.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 45 must be divided to get a perfect square?
  37. 37.A square garden has an area of 36 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 49 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 121 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 75 must be multiplied to get a perfect square?

Answer key

  1. 82
  2. 289
  3. 28
  4. 76
  5. 1444
  6. 54
  7. 169
  8. 196
  9. 256
  10. 71
  11. 35
  12. 15
  13. 14
  14. 3
  15. 1521
  16. 49
  17. 400
  18. 10
  19. 225
  20. 98
  21. 15
  22. 729
  23. 11
  24. 46
  25. 36
  26. 95
  27. 42
  28. 289
  29. 53
  30. 31
  31. 70
  32. 70
  33. 11
  34. 1089
  35. 14
  36. 5
  37. 6
  38. 7
  39. 11
  40. 3

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