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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 510 · 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 √841? =
  2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 34² and 35²?
  4. 4.How many whole numbers lie between 31² and 32²?
  5. 5.Which of these is a perfect square? (a) 324 (b) 350 (c) 360
  6. 6.What is √1521? =
  7. 7.What is 62²? =
  8. 8.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  9. 9.How many whole numbers lie between 48² and 49²?
  10. 10.How many whole numbers lie between 28² and 29²?
  11. 11.A square garden has an area of 1296 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 295 (b) 289 (c) 293
  13. 13.A square garden has an area of 3600 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 144 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  16. 16.What is √8649? =
  17. 17.How many whole numbers lie between 39² and 40²?
  18. 18.What is √6724? =
  19. 19.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 1024 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 35² and 36²?
  22. 22.What is 75²? =
  23. 23.A square garden has an area of 49 square m. How long is each side (in m)?
  24. 24.What is √1444? =
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 64²? =
  27. 27.How many whole numbers lie between 29² and 30²?
  28. 28.A square garden has an area of 121 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 18² and 19²?
  30. 30.What is √4900? =
  31. 31.A square garden has an area of 400 square m. How long is each side (in m)?
  32. 32.What is √9025? =
  33. 33.What is √1369? =
  34. 34.A square garden has an area of 36 square m. How long is each side (in m)?
  35. 35.What is 74²? =
  36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 15²? =
  38. 38.What is √7225? =
  39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  40. 40.How many whole numbers lie between 16² and 17²?

Answer key

  1. 29
  2. 196
  3. 68
  4. 62
  5. 324
  6. 39
  7. 3844
  8. 2
  9. 96
  10. 56
  11. 36
  12. 289
  13. 60
  14. 12
  15. 14
  16. 93
  17. 78
  18. 82
  19. 6
  20. 32
  21. 70
  22. 5625
  23. 7
  24. 38
  25. 324
  26. 4096
  27. 58
  28. 11
  29. 36
  30. 70
  31. 20
  32. 95
  33. 37
  34. 6
  35. 5476
  36. 225
  37. 225
  38. 85
  39. 484
  40. 32

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