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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 425 · 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 14²? =
  2. 2.What is √1225? =
  3. 3.How many whole numbers lie between 13² and 14²?
  4. 4.What is the smallest whole number by which 640 must be divided to get a perfect square?
  5. 5.What is 69²? =
  6. 6.What is 39²? =
  7. 7.What is √1024? =
  8. 8.Which of these is a perfect square? (a) 1313 (b) 1296 (c) 1310
  9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 100 square m. How long is each side (in m)?
  11. 11.What is 19²? =
  12. 12.What is √3249? =
  13. 13.What is 70²? =
  14. 14.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √8649? =
  16. 16.Which of these is a perfect square? (a) 135 (b) 136 (c) 121
  17. 17.What is √2601? =
  18. 18.How many whole numbers lie between 38² and 39²?
  19. 19.What is 73²? =
  20. 20.A square garden has an area of 441 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 200 (b) 205 (c) 196
  22. 22.What is 24²? =
  23. 23.How many whole numbers lie between 31² and 32²?
  24. 24.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  25. 25.A square garden has an area of 64 square m. How long is each side (in m)?
  26. 26.A square garden has an area of 324 square m. How long is each side (in m)?
  27. 27.Which of these is a perfect square? (a) 946 (b) 957 (c) 900
  28. 28.What is √8100? =
  29. 29.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  30. 30.How many whole numbers lie between 30² and 31²?
  31. 31.What is √3844? =
  32. 32.What is 17²? =
  33. 33.How many whole numbers lie between 40² and 41²?
  34. 34.Which of these is a perfect square? (a) 148 (b) 145 (c) 144
  35. 35.A square garden has an area of 1681 square m. How long is each side (in m)?
  36. 36.What is 85²? =
  37. 37.What is √3364? =
  38. 38.What is √1296? =
  39. 39.What is √5329? =
  40. 40.What is 56²? =

Answer key

  1. 196
  2. 35
  3. 26
  4. 10
  5. 4761
  6. 1521
  7. 32
  8. 1296
  9. 529
  10. 10
  11. 361
  12. 57
  13. 4900
  14. 484
  15. 93
  16. 121
  17. 51
  18. 76
  19. 5329
  20. 21
  21. 196
  22. 576
  23. 62
  24. 15
  25. 8
  26. 18
  27. 900
  28. 90
  29. 3
  30. 60
  31. 62
  32. 289
  33. 80
  34. 144
  35. 41
  36. 7225
  37. 58
  38. 36
  39. 73
  40. 3136

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