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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 23 · 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 √7396? =
  2. 2.Which of these is a perfect square? (a) 765 (b) 782 (c) 729
  3. 3.Which of these is a perfect square? (a) 256 (b) 265 (c) 278
  4. 4.How many whole numbers lie between 21² and 22²?
  5. 5.How many whole numbers lie between 41² and 42²?
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 164 (b) 144 (c) 149
  8. 8.What is 29²? =
  9. 9.What is √1156? =
  10. 10.A square garden has an area of 64 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 1681 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 676 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 529 square m. How long is each side (in m)?
  14. 14.What is 39²? =
  15. 15.What is 45²? =
  16. 16.Which of these is a perfect square? (a) 1662 (b) 1600 (c) 1645
  17. 17.How many whole numbers lie between 11² and 12²?
  18. 18.How many whole numbers lie between 45² and 46²?
  19. 19.Which of these is a perfect square? (a) 1338 (b) 1355 (c) 1296
  20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is 46²? =
  22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 15² and 16²?
  24. 24.Which of these is a perfect square? (a) 171 (b) 184 (c) 169
  25. 25.What is 32²? =
  26. 26.What is √2025? =
  27. 27.What is √2601? =
  28. 28.How many whole numbers lie between 38² and 39²?
  29. 29.Which of these is a perfect square? (a) 337 (b) 357 (c) 324
  30. 30.How many whole numbers lie between 28² and 29²?
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √256? =
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the smallest whole number by which 275 must be divided to get a perfect square?
  36. 36.Which of these is a perfect square? (a) 1160 (b) 1156 (c) 1188
  37. 37.What is √3481? =
  38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 25² and 26²?
  40. 40.What is the smallest whole number by which 117 must be multiplied to get a perfect square?

Answer key

  1. 86
  2. 729
  3. 256
  4. 42
  5. 82
  6. 256
  7. 144
  8. 841
  9. 34
  10. 8
  11. 41
  12. 26
  13. 23
  14. 1521
  15. 2025
  16. 1600
  17. 22
  18. 90
  19. 1296
  20. 441
  21. 2116
  22. 576
  23. 30
  24. 169
  25. 1024
  26. 45
  27. 51
  28. 76
  29. 324
  30. 56
  31. 64
  32. 16
  33. 144
  34. 121
  35. 11
  36. 1156
  37. 59
  38. 54
  39. 50
  40. 13

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