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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 323 · 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 smallest whole number by which 320 must be divided to get a perfect square?
  2. 2.What is √576? =
  3. 3.How many whole numbers lie between 32² and 33²?
  4. 4.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  5. 5.What is √4096? =
  6. 6.Which of these is a perfect square? (a) 400 (b) 439 (c) 412
  7. 7.Which of these is a perfect square? (a) 1289 (b) 1288 (c) 1225
  8. 8.Which of these is a perfect square? (a) 256 (b) 269 (c) 264
  9. 9.What is 59²? =
  10. 10.What is 80²? =
  11. 11.What is √8464? =
  12. 12.A square garden has an area of 3364 square m. How long is each side (in m)?
  13. 13.How many whole numbers lie between 11² and 12²?
  14. 14.What is 15²? =
  15. 15.What is the smallest whole number by which 20 must be divided to get a perfect square?
  16. 16.Which of these is a perfect square? (a) 209 (b) 202 (c) 196
  17. 17.A square garden has an area of 1849 square m. How long is each side (in m)?
  18. 18.What is 45²? =
  19. 19.What is √2401? =
  20. 20.Which of these is a perfect square? (a) 100 (b) 102 (c) 119
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 2401 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 1197 (b) 1156 (c) 1217
  24. 24.What is 35²? =
  25. 25.What is 23²? =
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is 85²? =
  28. 28.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  29. 29.What is √484? =
  30. 30.What is 49²? =
  31. 31.What is the smallest whole number by which 245 must be divided to get a perfect square?
  32. 32.A square garden has an area of 529 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 27² and 28²?
  35. 35.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  36. 36.How many whole numbers lie between 13² and 14²?
  37. 37.How many whole numbers lie between 23² and 24²?
  38. 38.A square garden has an area of 1225 square m. How long is each side (in m)?
  39. 39.What is 32²? =
  40. 40.What is √9409? =

Answer key

  1. 5
  2. 24
  3. 64
  4. 10
  5. 64
  6. 400
  7. 1225
  8. 256
  9. 3481
  10. 6400
  11. 92
  12. 58
  13. 22
  14. 225
  15. 5
  16. 196
  17. 43
  18. 2025
  19. 49
  20. 100
  21. 576
  22. 49
  23. 1156
  24. 1225
  25. 529
  26. 100
  27. 7225
  28. 10
  29. 22
  30. 2401
  31. 5
  32. 23
  33. 64
  34. 54
  35. 5
  36. 26
  37. 46
  38. 35
  39. 1024
  40. 97

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