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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 337 · 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 25 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is 21²? =
  3. 3.What is 37²? =
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 20² and 21²?
  6. 6.A square garden has an area of 784 square m. How long is each side (in m)?
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 256 (b) 280 (c) 267
  9. 9.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 382 (b) 361 (c) 372
  11. 11.Which of these is a perfect square? (a) 1024 (b) 1063 (c) 1079
  12. 12.What is √5929? =
  13. 13.Which of these is a perfect square? (a) 145 (b) 161 (c) 144
  14. 14.A square garden has an area of 2209 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 484 (b) 512 (c) 492
  16. 16.How many whole numbers lie between 32² and 33²?
  17. 17.What is 70²? =
  18. 18.How many whole numbers lie between 11² and 12²?
  19. 19.What is √6241? =
  20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √2500? =
  22. 22.What is √625? =
  23. 23.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 32²? =
  25. 25.What is 49²? =
  26. 26.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  27. 27.What is √8649? =
  28. 28.A square garden has an area of 1764 square m. How long is each side (in m)?
  29. 29.What is 76²? =
  30. 30.Which of these is a perfect square? (a) 126 (b) 121 (c) 135
  31. 31.How many whole numbers lie between 49² and 50²?
  32. 32.What is √441? =
  33. 33.How many whole numbers lie between 37² and 38²?
  34. 34.Which of these is a perfect square? (a) 931 (b) 900 (c) 905
  35. 35.How many whole numbers lie between 26² and 27²?
  36. 36.A square garden has an area of 1521 square m. How long is each side (in m)?
  37. 37.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  38. 38.A square garden has an area of 2116 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 14² and 15²?
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 625
  2. 441
  3. 1369
  4. 121
  5. 40
  6. 28
  7. 49
  8. 256
  9. 36
  10. 361
  11. 1024
  12. 77
  13. 144
  14. 47
  15. 484
  16. 64
  17. 4900
  18. 22
  19. 79
  20. 676
  21. 50
  22. 25
  23. 900
  24. 1024
  25. 2401
  26. 2
  27. 93
  28. 42
  29. 5776
  30. 121
  31. 98
  32. 21
  33. 74
  34. 900
  35. 52
  36. 39
  37. 3
  38. 46
  39. 28
  40. 100

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