Q. 524.8( 9 Votes )

If p is a prime number then prove that √p is irrational.

Answer :

let us suppose that is a rational number.

thenwhere also a and b is rational and b ≠ 0


on squaring both sides,we get,





Let a = pr, for some integer r






Thus p is a common factor of a and b.


But this is a contradiction since a and b have no common factor as they are prime numbers


This is the contradiction to our assumption


Hence, √p is irrational.


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