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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 395 · 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 74²? =
  2. 2.Which of these is a perfect square? (a) 121 (b) 126 (c) 123
  3. 3.How many whole numbers lie between 26² and 27²?
  4. 4.A square garden has an area of 484 square m. How long is each side (in m)?
  5. 5.What is 45²? =
  6. 6.Which of these is a perfect square? (a) 967 (b) 1015 (c) 961
  7. 7.A square garden has an area of 1444 square m. How long is each side (in m)?
  8. 8.What is 36²? =
  9. 9.What is the smallest whole number by which 50 must be divided to get a perfect square?
  10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is √900? =
  12. 12.Which of these is a perfect square? (a) 1664 (b) 1600 (c) 1648
  13. 13.What is 22²? =
  14. 14.Which of these is a perfect square? (a) 475 (b) 441 (c) 477
  15. 15.How many whole numbers lie between 20² and 21²?
  16. 16.How many whole numbers lie between 36² and 37²?
  17. 17.A square garden has an area of 2025 square m. How long is each side (in m)?
  18. 18.A square garden has an area of 1296 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 234 (b) 243 (c) 225
  21. 21.Which of these is a perfect square? (a) 539 (b) 529 (c) 573
  22. 22.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 311 (b) 289 (c) 302
  24. 24.How many whole numbers lie between 16² and 17²?
  25. 25.What is 57²? =
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 169 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 1936 square m. How long is each side (in m)?
  29. 29.What is √3025? =
  30. 30.How many whole numbers lie between 38² and 39²?
  31. 31.Which of these is a perfect square? (a) 1541 (b) 1521 (c) 1564
  32. 32.What is 91²? =
  33. 33.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  34. 34.What is √1369? =
  35. 35.What is 39²? =
  36. 36.What is √4489? =
  37. 37.What is the smallest whole number by which 448 must be divided to get a perfect square?
  38. 38.What is 59²? =
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is 42²? =

Answer key

  1. 5476
  2. 121
  3. 52
  4. 22
  5. 2025
  6. 961
  7. 38
  8. 1296
  9. 2
  10. 484
  11. 30
  12. 1600
  13. 484
  14. 441
  15. 40
  16. 72
  17. 45
  18. 36
  19. 15
  20. 225
  21. 529
  22. 5
  23. 289
  24. 32
  25. 3249
  26. 529
  27. 13
  28. 44
  29. 55
  30. 76
  31. 1521
  32. 8281
  33. 3
  34. 37
  35. 1521
  36. 67
  37. 7
  38. 3481
  39. 100
  40. 1764

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