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Can someone explain me how to find square root by prime factorization ?

1 Answer

2 votes

Answer:

STEPS

  • Step I: Obtain the given number.
  • Step II: Resolve the given number into prime factors by successive division.
  • Step III: Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
  • Step IV: Take one factor from each pair.
  • Step V: Find the product of factors obtained in step IV.
  • Step VI: The product obtained in step V is the required square root.

Example

Find the square root of 324

  • 324 = 2 x 162
  • = 2 x 2 x 81
  • = 2 x 2 x 3 x 27
  • = 2 x 2 x 3 x 3 x 9
  • = 2 x 2 x 3 x 3 x 3 x 3
  • ∴ √324 = √( 2 x 2 x 3 x 3 x 3 x 3 )
  • √324 = 2 x 3 x 3
  • √324 = 18
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