Question

Prove that root6 + root2 is an irrational number .

Answer 1

let √6+√2 be rational number
√6+√2=p/q
√2=p/q-√6
√2=p-√q6/q
S.O.B.S
2=p^2+36q-12√6/q^2
2q^2-p^2-36q=-12√6
√6=2q^2-p^2-36q/-12
as 2q^2-p^2-36q/-12 is in p/q form it is rational number so √6 should be rational number
but in general √6 is irrational.
so our assumption is wrong
it is a contradiction
therefore √6+√2 is an irrational number