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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 22 · 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) 994 (b) 961 (c) 985
  2. 2.Which of these is a perfect square? (a) 488 (b) 505 (c) 484
  3. 3.Which of these is a perfect square? (a) 147 (b) 154 (c) 144
  4. 4.What is √289? =
  5. 5.How many whole numbers lie between 25² and 26²?
  6. 6.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  8. 8.A square garden has an area of 529 square m. How long is each side (in m)?
  9. 9.What is 38²? =
  10. 10.What is √3249? =
  11. 11.What is 69²? =
  12. 12.Which of these is a perfect square? (a) 611 (b) 600 (c) 576
  13. 13.What is 74²? =
  14. 14.A square garden has an area of 2025 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  16. 16.Which of these is a perfect square? (a) 1523 (b) 1521 (c) 1539
  17. 17.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  18. 18.What is the smallest whole number by which 252 must be divided to get a perfect square?
  19. 19.A square garden has an area of 256 square m. How long is each side (in m)?
  20. 20.What is √1024? =
  21. 21.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  22. 22.What is √1156? =
  23. 23.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √6889? =
  25. 25.What is 72²? =
  26. 26.How many whole numbers lie between 36² and 37²?
  27. 27.Which of these is a perfect square? (a) 361 (b) 366 (c) 369
  28. 28.Which of these is a perfect square? (a) 636 (b) 625 (c) 640
  29. 29.What is √225? =
  30. 30.Which of these is a perfect square? (a) 1670 (b) 1600 (c) 1612
  31. 31.How many whole numbers lie between 18² and 19²?
  32. 32.Which of these is a perfect square? (a) 215 (b) 202 (c) 196
  33. 33.What is 64²? =
  34. 34.What is √529? =
  35. 35.How many whole numbers lie between 49² and 50²?
  36. 36.What is 29²? =
  37. 37.What is √2500? =
  38. 38.A square garden has an area of 100 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  40. 40.What is √3721? =

Answer key

  1. 961
  2. 484
  3. 144
  4. 17
  5. 50
  6. 576
  7. 324
  8. 23
  9. 1444
  10. 57
  11. 4761
  12. 576
  13. 5476
  14. 45
  15. 3
  16. 1521
  17. 10
  18. 7
  19. 16
  20. 32
  21. 14
  22. 34
  23. 81
  24. 83
  25. 5184
  26. 72
  27. 361
  28. 625
  29. 15
  30. 1600
  31. 36
  32. 196
  33. 4096
  34. 23
  35. 98
  36. 841
  37. 50
  38. 10
  39. 13
  40. 61

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