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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 628 · 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) 144 (b) 145 (c) 163
  2. 2.How many whole numbers lie between 49² and 50²?
  3. 3.How many whole numbers lie between 47² and 48²?
  4. 4.How many whole numbers lie between 27² and 28²?
  5. 5.What is 90²? =
  6. 6.How many whole numbers lie between 16² and 17²?
  7. 7.What is the smallest whole number by which 162 must be divided to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 1604 (b) 1625 (c) 1600
  9. 9.A square garden has an area of 1764 square m. How long is each side (in m)?
  10. 10.A square garden has an area of 1024 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 7² and 8²?
  16. 16.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 20² and 21²?
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  19. 19.A square garden has an area of 144 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 1266 (b) 1259 (c) 1225
  21. 21.Which of these is a perfect square? (a) 915 (b) 900 (c) 947
  22. 22.What is 93²? =
  23. 23.Which of these is a perfect square? (a) 625 (b) 630 (c) 646
  24. 24.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  25. 25.What is √484? =
  26. 26.What is √5776? =
  27. 27.Which of these is a perfect square? (a) 794 (b) 817 (c) 784
  28. 28.What is √1681? =
  29. 29.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  30. 30.What is the smallest whole number by which 735 must be divided to get a perfect square?
  31. 31.What is 78²? =
  32. 32.What is √4624? =
  33. 33.What is √5329? =
  34. 34.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 36 square m. How long is each side (in m)?
  36. 36.A square garden has an area of 1600 square m. How long is each side (in m)?
  37. 37.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  38. 38.What is √2916? =
  39. 39.What is 19²? =
  40. 40.What is √144? =

Answer key

  1. 144
  2. 98
  3. 94
  4. 54
  5. 8100
  6. 32
  7. 2
  8. 1600
  9. 42
  10. 32
  11. 36
  12. 784
  13. 256
  14. 729
  15. 14
  16. 625
  17. 40
  18. 676
  19. 12
  20. 1225
  21. 900
  22. 8649
  23. 625
  24. 5
  25. 22
  26. 76
  27. 784
  28. 41
  29. 6
  30. 15
  31. 6084
  32. 68
  33. 73
  34. 144
  35. 6
  36. 40
  37. 15
  38. 54
  39. 361
  40. 12

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