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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 600 · 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.A square garden has an area of 1225 square m. How long is each side (in m)?
  2. 2.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √7744? =
  6. 6.What is 18²? =
  7. 7.Which of these is a perfect square? (a) 1609 (b) 1665 (c) 1600
  8. 8.What is 48²? =
  9. 9.Which of these is a perfect square? (a) 544 (b) 535 (c) 529
  10. 10.A square garden has an area of 1849 square m. How long is each side (in m)?
  11. 11.Which of these is a perfect square? (a) 1079 (b) 1071 (c) 1024
  12. 12.How many whole numbers lie between 13² and 14²?
  13. 13.What is √3481? =
  14. 14.What is 66²? =
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  18. 18.A square garden has an area of 1521 square m. How long is each side (in m)?
  19. 19.Which of these is a perfect square? (a) 417 (b) 400 (c) 429
  20. 20.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √1600? =
  22. 22.A square garden has an area of 100 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 35² and 36²?
  24. 24.Which of these is a perfect square? (a) 1438 (b) 1410 (c) 1369
  25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 57²? =
  27. 27.What is 76²? =
  28. 28.What is √1024? =
  29. 29.Which of these is a perfect square? (a) 880 (b) 882 (c) 841
  30. 30.What is 91²? =
  31. 31.Which of these is a perfect square? (a) 1574 (b) 1521 (c) 1528
  32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  33. 33.A square garden has an area of 1764 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 18² and 19²?
  35. 35.What is 11²? =
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 196 square m. How long is each side (in m)?
  38. 38.What is √6724? =
  39. 39.A square garden has an area of 3025 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 1156 square m. How long is each side (in m)?

Answer key

  1. 35
  2. 13
  3. 100
  4. 256
  5. 88
  6. 324
  7. 1600
  8. 2304
  9. 529
  10. 43
  11. 1024
  12. 26
  13. 59
  14. 4356
  15. 400
  16. 676
  17. 15
  18. 39
  19. 400
  20. 841
  21. 40
  22. 10
  23. 70
  24. 1369
  25. 484
  26. 3249
  27. 5776
  28. 32
  29. 841
  30. 8281
  31. 1521
  32. 144
  33. 42
  34. 36
  35. 121
  36. 625
  37. 14
  38. 82
  39. 55
  40. 34

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