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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 454 · 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 the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √6724? =
  3. 3.What is 16²? =
  4. 4.Which of these is a perfect square? (a) 967 (b) 966 (c) 961
  5. 5.How many whole numbers lie between 11² and 12²?
  6. 6.What is the smallest whole number by which 192 must be divided to get a perfect square?
  7. 7.What is the smallest whole number by which 135 must be divided to get a perfect square?
  8. 8.A square garden has an area of 625 square m. How long is each side (in m)?
  9. 9.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 17²? =
  11. 11.How many whole numbers lie between 29² and 30²?
  12. 12.How many whole numbers lie between 18² and 19²?
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 12² and 13²?
  15. 15.What is the smallest whole number by which 18 must be divided to get a perfect square?
  16. 16.A square garden has an area of 2209 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  18. 18.What is 90²? =
  19. 19.Which of these is a perfect square? (a) 729 (b) 753 (c) 776
  20. 20.What is √1024? =
  21. 21.What is √121? =
  22. 22.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  23. 23.A square garden has an area of 64 square m. How long is each side (in m)?
  24. 24.What is 40²? =
  25. 25.How many whole numbers lie between 33² and 34²?
  26. 26.Which of these is a perfect square? (a) 1268 (b) 1225 (c) 1276
  27. 27.A square garden has an area of 169 square m. How long is each side (in m)?
  28. 28.What is 59²? =
  29. 29.What is √4761? =
  30. 30.Which of these is a perfect square? (a) 260 (b) 256 (c) 263
  31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 37² and 38²?
  33. 33.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  35. 35.What is √5476? =
  36. 36.What is √5625? =
  37. 37.What is √1369? =
  38. 38.What is √3025? =
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 784
  2. 82
  3. 256
  4. 961
  5. 22
  6. 3
  7. 15
  8. 25
  9. 324
  10. 289
  11. 58
  12. 36
  13. 400
  14. 24
  15. 2
  16. 47
  17. 15
  18. 8100
  19. 729
  20. 32
  21. 11
  22. 3
  23. 8
  24. 1600
  25. 66
  26. 1225
  27. 13
  28. 3481
  29. 69
  30. 256
  31. 25
  32. 74
  33. 676
  34. 5
  35. 74
  36. 75
  37. 37
  38. 55
  39. 100
  40. 196

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