Question

proof 6+√2is rational

Answer 1

hey may i tell u nikhil there must be a question to prove 6+√2 as an irrational no.
but,you asked here its a rational no. ,
so please verify your question
thank you :)

Answer 2

I'm assuming that you mean to ask to prove that 6+ √2 is an irrational or not rational.

Let's prove it by contradiction method.

Suppose that 6 + √2 is a rational number.

6+√2= p (which is rational)
(6+√2)^2 = p^2
36+2+12√2= p^2
38+12√2= p^2
√2 = (38-p^2)/12

(38-p^2)/12 is rational.
So √2 is rational. But √2 is irrational.

We reach at a contradiction which means our supposition is wrong. 6+√2 is not rational.