state root6+root2 is irrational

let √6+√2 be rational

this implies (√6+√2)^2 is rational.

this implies 6+2+2√12= 8+2√12 is rational.

but √12 is irrational.

this implies 2√12 is irrational. so, 8+2√12 is irrational.

so our assumption was wrong.

hence √6+√2 is irrational.