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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 585 · 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 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 484 (b) 494 (c) 490
  3. 3.How many whole numbers lie between 14² and 15²?
  4. 4.What is √2601? =
  5. 5.How many whole numbers lie between 27² and 28²?
  6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 1309 (b) 1316 (c) 1296
  8. 8.What is 56²? =
  9. 9.What is 28²? =
  10. 10.What is √2304? =
  11. 11.Which of these is a perfect square? (a) 270 (b) 256 (c) 271
  12. 12.What is the smallest whole number by which 108 must be divided to get a perfect square?
  13. 13.A square garden has an area of 1936 square m. How long is each side (in m)?
  14. 14.How many whole numbers lie between 12² and 13²?
  15. 15.Which of these is a perfect square? (a) 807 (b) 810 (c) 784
  16. 16.How many whole numbers lie between 41² and 42²?
  17. 17.Which of these is a perfect square? (a) 136 (b) 128 (c) 121
  18. 18.What is √6400? =
  19. 19.What is 99²? =
  20. 20.What is the smallest whole number by which 48 must be divided to get a perfect square?
  21. 21.What is 59²? =
  22. 22.What is √1764? =
  23. 23.What is 53²? =
  24. 24.How many whole numbers lie between 10² and 11²?
  25. 25.How many whole numbers lie between 40² and 41²?
  26. 26.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 81²? =
  29. 29.What is √2116? =
  30. 30.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 39² and 40²?
  32. 32.What is 25²? =
  33. 33.A square garden has an area of 36 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 45² and 46²?
  35. 35.A square garden has an area of 1156 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 17² and 18²?
  37. 37.How many whole numbers lie between 20² and 21²?
  38. 38.Which of these is a perfect square? (a) 667 (b) 646 (c) 625
  39. 39.A square garden has an area of 961 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 1093 (b) 1089 (c) 1096

Answer key

  1. 36
  2. 484
  3. 28
  4. 51
  5. 54
  6. 144
  7. 1296
  8. 3136
  9. 784
  10. 48
  11. 256
  12. 3
  13. 44
  14. 24
  15. 784
  16. 82
  17. 121
  18. 80
  19. 9801
  20. 3
  21. 3481
  22. 42
  23. 2809
  24. 20
  25. 80
  26. 15
  27. 361
  28. 6561
  29. 46
  30. 10
  31. 78
  32. 625
  33. 6
  34. 90
  35. 34
  36. 34
  37. 40
  38. 625
  39. 31
  40. 1089

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