Question

prove that the sum of rational number and irrational number is irrational number

Answer 1

root 2+2=root 2+2
which is an irrational no.
but root 2+root 2=2 root 2 which is also an irrational number 
but 2+2=4 which is rational number 
and that why rational+rational=rational
irrational+rational=irrational and irrational+irrational is also irrational