Question

Prime that √x+√y is irrational ,where x and y are primes.

Answer 1

let assume X +√y be rational no. 
then x+√y=p/q (Where p and q are integers and co-prime) 
=> √y= p/q- x
=> √y is rational no.
but, it contradict the fact √y is. irrational (I. e. given in question) 
hence, contradiction ,so x+√y is irrational. Thanks