Question

prove that √p is irrational..​

Answer 1

let us assume on the contrary that √p is a rational no. then there exist positive co primes a and b such that.

√p = p/q

squarring both side

=》 p = a^2/b^2

=》b^2p = a^2

=》 p/a^2

=》 p/a

=》 a = p × c

Now, b^2p = a^2

=》 b^2p = p^2c^2

=》 b^2 = pc^2

=》 p/b^2

=》 p/b

Therefore 'a' and 'b' are not co primes as p is a factor of both 'a' and 'b' this contradiction has been arised due to our wrong assumption that √p is a rational no. hence √p is a irrational no.

proved

♡maverick ☆