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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 621 · 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.Which of these is a perfect square? (a) 344 (b) 333 (c) 324
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 900 square m. How long is each side (in m)?
  4. 4.What is √169? =
  5. 5.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  6. 6.What is the smallest whole number by which 117 must be divided to get a perfect square?
  7. 7.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  8. 8.A square garden has an area of 100 square m. How long is each side (in m)?
  9. 9.What is 35²? =
  10. 10.What is √3969? =
  11. 11.A square garden has an area of 2209 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 46² and 47²?
  13. 13.What is 23²? =
  14. 14.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  15. 15.A square garden has an area of 625 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 36 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 1089 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 39² and 40²?
  19. 19.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  20. 20.What is √1296? =
  21. 21.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 1446 (b) 1469 (c) 1444
  23. 23.What is √729? =
  24. 24.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 1089 (b) 1106 (c) 1091
  26. 26.How many whole numbers lie between 9² and 10²?
  27. 27.Which of these is a perfect square? (a) 625 (b) 630 (c) 628
  28. 28.What is √1681? =
  29. 29.What is √625? =
  30. 30.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √6241? =
  33. 33.Which of these is a perfect square? (a) 1571 (b) 1521 (c) 1552
  34. 34.What is √4761? =
  35. 35.What is √9409? =
  36. 36.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 484 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 15² and 16²?
  39. 39.How many whole numbers lie between 38² and 39²?
  40. 40.Which of these is a perfect square? (a) 100 (b) 102 (c) 115

Answer key

  1. 324
  2. 81
  3. 30
  4. 13
  5. 13
  6. 13
  7. 13
  8. 10
  9. 1225
  10. 63
  11. 47
  12. 92
  13. 529
  14. 5
  15. 25
  16. 6
  17. 33
  18. 78
  19. 5
  20. 36
  21. 11
  22. 1444
  23. 27
  24. 3
  25. 1089
  26. 18
  27. 625
  28. 41
  29. 25
  30. 13
  31. 841
  32. 79
  33. 1521
  34. 69
  35. 97
  36. 256
  37. 22
  38. 30
  39. 76
  40. 100

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