Question

prove that
$6 + \sqrt{2} \: is \: irrational$
​

Answer 1

Hello!!☺

Let us assume that 6+√2 is rational so,

6+√2 =$\frac{p}{q}$ (where p and q are co-prime)

√2=$\frac{p}{q} -6$

√2=$\frac{p-6q}{q}$

In this case, L.H.S is irrational while R.H.S is rational. Actually, L.H.S≠R.H.S.

So, this is a contradiction in our assumption hence, 6+√2 is irrational.