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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 532 · 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 10 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √1936? =
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 23²? =
  5. 5.Which of these is a perfect square? (a) 144 (b) 158 (c) 148
  6. 6.Which of these is a perfect square? (a) 308 (b) 296 (c) 289
  7. 7.What is √196? =
  8. 8.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 817 (b) 784 (c) 831
  10. 10.What is √1764? =
  11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 22² and 23²?
  13. 13.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  14. 14.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  15. 15.How many whole numbers lie between 27² and 28²?
  16. 16.A square garden has an area of 2916 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 125 must be divided to get a perfect square?
  18. 18.What is 19²? =
  19. 19.How many whole numbers lie between 31² and 32²?
  20. 20.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the smallest whole number by which 48 must be divided to get a perfect square?
  22. 22.What is 22²? =
  23. 23.How many whole numbers lie between 7² and 8²?
  24. 24.What is √2401? =
  25. 25.What is 44²? =
  26. 26.A square garden has an area of 1024 square m. How long is each side (in m)?
  27. 27.What is 84²? =
  28. 28.A square garden has an area of 3249 square m. How long is each side (in m)?
  29. 29.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 15² and 16²?
  31. 31.A square garden has an area of 144 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 554 (b) 556 (c) 529
  33. 33.Which of these is a perfect square? (a) 453 (b) 441 (c) 442
  34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  35. 35.How many whole numbers lie between 45² and 46²?
  36. 36.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  37. 37.How many whole numbers lie between 20² and 21²?
  38. 38.What is the smallest whole number by which 640 must be divided to get a perfect square?
  39. 39.What is 92²? =
  40. 40.What is the smallest whole number by which 128 must be multiplied to get a perfect square?

Answer key

  1. 100
  2. 44
  3. 225
  4. 529
  5. 144
  6. 289
  7. 14
  8. 729
  9. 784
  10. 42
  11. 121
  12. 44
  13. 14
  14. 3
  15. 54
  16. 54
  17. 5
  18. 361
  19. 62
  20. 324
  21. 3
  22. 484
  23. 14
  24. 49
  25. 1936
  26. 32
  27. 7056
  28. 57
  29. 784
  30. 30
  31. 12
  32. 529
  33. 441
  34. 81
  35. 90
  36. 5
  37. 40
  38. 10
  39. 8464
  40. 2

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