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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 185 · 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 400 square m. How long is each side (in m)?
  2. 2.What is √1444? =
  3. 3.Which of these is a perfect square? (a) 1225 (b) 1239 (c) 1284
  4. 4.How many whole numbers lie between 18² and 19²?
  5. 5.Which of these is a perfect square? (a) 1321 (b) 1339 (c) 1296
  6. 6.How many whole numbers lie between 45² and 46²?
  7. 7.How many whole numbers lie between 38² and 39²?
  8. 8.How many whole numbers lie between 9² and 10²?
  9. 9.A square garden has an area of 1089 square m. How long is each side (in m)?
  10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 44² and 45²?
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  15. 15.What is 19²? =
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 36² and 37²?
  18. 18.A square garden has an area of 625 square m. How long is each side (in m)?
  19. 19.A square garden has an area of 1444 square m. How long is each side (in m)?
  20. 20.What is √361? =
  21. 21.What is 50²? =
  22. 22.A square garden has an area of 36 square m. How long is each side (in m)?
  23. 23.What is 26²? =
  24. 24.What is √121? =
  25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √2809? =
  27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 29²? =
  29. 29.What is 52²? =
  30. 30.What is √169? =
  31. 31.What is √8836? =
  32. 32.A square garden has an area of 1024 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 18²? =
  35. 35.What is √1225? =
  36. 36.Which of these is a perfect square? (a) 398 (b) 364 (c) 361
  37. 37.A square garden has an area of 361 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 8² and 9²?
  39. 39.What is √7225? =
  40. 40.What is the smallest whole number by which 208 must be divided to get a perfect square?

Answer key

  1. 20
  2. 38
  3. 1225
  4. 36
  5. 1296
  6. 90
  7. 76
  8. 18
  9. 33
  10. 361
  11. 576
  12. 88
  13. 64
  14. 3
  15. 361
  16. 784
  17. 72
  18. 25
  19. 38
  20. 19
  21. 2500
  22. 6
  23. 676
  24. 11
  25. 729
  26. 53
  27. 100
  28. 841
  29. 2704
  30. 13
  31. 94
  32. 32
  33. 25
  34. 324
  35. 35
  36. 361
  37. 19
  38. 16
  39. 85
  40. 13

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