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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 496 · 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 84²? =
  2. 2.What is 65²? =
  3. 3.A square garden has an area of 576 square m. How long is each side (in m)?
  4. 4.What is 66²? =
  5. 5.How many whole numbers lie between 11² and 12²?
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 421 (b) 400 (c) 404
  8. 8.Which of these is a perfect square? (a) 169 (b) 174 (c) 179
  9. 9.Which of these is a perfect square? (a) 272 (b) 283 (c) 256
  10. 10.What is 72²? =
  11. 11.What is √841? =
  12. 12.How many whole numbers lie between 18² and 19²?
  13. 13.A square garden has an area of 2916 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 1936 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 637 must be divided to get a perfect square?
  16. 16.What is √1296? =
  17. 17.What is √2304? =
  18. 18.What is 44²? =
  19. 19.A square garden has an area of 289 square m. How long is each side (in m)?
  20. 20.What is √7921? =
  21. 21.A square garden has an area of 3025 square m. How long is each side (in m)?
  22. 22.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 38² and 39²?
  24. 24.What is 27²? =
  25. 25.What is 40²? =
  26. 26.Which of these is a perfect square? (a) 144 (b) 150 (c) 152
  27. 27.A square garden has an area of 49 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 39² and 40²?
  29. 29.What is √441? =
  30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  31. 31.A square garden has an area of 225 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 576 (b) 590 (c) 619
  33. 33.What is 36²? =
  34. 34.What is √3721? =
  35. 35.A square garden has an area of 1024 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 1513 (b) 1474 (c) 1444
  37. 37.What is 87²? =
  38. 38.How many whole numbers lie between 15² and 16²?
  39. 39.How many whole numbers lie between 10² and 11²?
  40. 40.Which of these is a perfect square? (a) 229 (b) 225 (c) 241

Answer key

  1. 7056
  2. 4225
  3. 24
  4. 4356
  5. 22
  6. 256
  7. 400
  8. 169
  9. 256
  10. 5184
  11. 29
  12. 36
  13. 54
  14. 44
  15. 13
  16. 36
  17. 48
  18. 1936
  19. 17
  20. 89
  21. 55
  22. 784
  23. 76
  24. 729
  25. 1600
  26. 144
  27. 7
  28. 78
  29. 21
  30. 36
  31. 15
  32. 576
  33. 1296
  34. 61
  35. 32
  36. 1444
  37. 7569
  38. 30
  39. 20
  40. 225

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