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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 257 · 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 3481 square m. How long is each side (in m)?
  2. 2.What is √2500? =
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 405 must be divided to get a perfect square?
  5. 5.A square garden has an area of 256 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 224 must be divided to get a perfect square?
  7. 7.How many whole numbers lie between 27² and 28²?
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √1369? =
  10. 10.How many whole numbers lie between 49² and 50²?
  11. 11.What is 60²? =
  12. 12.What is √400? =
  13. 13.Which of these is a perfect square? (a) 1380 (b) 1426 (c) 1369
  14. 14.What is the smallest whole number by which 60 must be divided to get a perfect square?
  15. 15.What is √289? =
  16. 16.A square garden has an area of 81 square m. How long is each side (in m)?
  17. 17.What is 87²? =
  18. 18.A square garden has an area of 1225 square m. How long is each side (in m)?
  19. 19.Which of these is a perfect square? (a) 625 (b) 626 (c) 633
  20. 20.A square garden has an area of 49 square m. How long is each side (in m)?
  21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  22. 22.Which of these is a perfect square? (a) 169 (b) 189 (c) 170
  23. 23.What is √1764? =
  24. 24.A square garden has an area of 324 square m. How long is each side (in m)?
  25. 25.What is √3721? =
  26. 26.What is √8464? =
  27. 27.What is the smallest whole number by which 90 must be divided to get a perfect square?
  28. 28.Which of these is a perfect square? (a) 255 (b) 244 (c) 225
  29. 29.What is the smallest whole number by which 24 must be divided to get a perfect square?
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √2116? =
  32. 32.What is 95²? =
  33. 33.How many whole numbers lie between 21² and 22²?
  34. 34.What is 47²? =
  35. 35.A square garden has an area of 144 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 1296 (b) 1365 (c) 1312
  37. 37.What is √1089? =
  38. 38.What is 92²? =
  39. 39.A square garden has an area of 225 square m. How long is each side (in m)?
  40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 59
  2. 50
  3. 196
  4. 5
  5. 16
  6. 14
  7. 54
  8. 144
  9. 37
  10. 98
  11. 3600
  12. 20
  13. 1369
  14. 15
  15. 17
  16. 9
  17. 7569
  18. 35
  19. 625
  20. 7
  21. 49
  22. 169
  23. 42
  24. 18
  25. 61
  26. 92
  27. 10
  28. 225
  29. 6
  30. 324
  31. 46
  32. 9025
  33. 42
  34. 2209
  35. 12
  36. 1296
  37. 33
  38. 8464
  39. 15
  40. 121

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