Question

√2+8 rational or irrational

Answer 1

it's irrational I think so

Answer 2

Let us assume to the contrary that √2+8 is rational therefore it has two coprimes a and b .
such that √2+8 = a/b
or √2 = a/b-8

in above a , b , and 8 are integers so they are rational ,and therefore√2 is rational but it contradicts the fact that √2 is irrational ,
this contradiction arose due to one incorrect assumption that √2+8 is rational and there fore √2+8 is rational .