Let us assume that 3−√5 is a rational number
Then. there exist coprime integers p, q,q≠0 such that
3−√5=pq
=>√5=3−pq
Here, 3−pq is a rational number, but √5 is a irrational number.
But, a irrational cannot be equal to a rational number.This is a contradiction.
Thus, our assumption is wrong.
Therefore 3−√5 is a irrational number.