#### Question :

Prove that 6 + √ 2 is irrationalSubmitted on 21/1/2024 | Answered by Vandana Rana#### Answer :

Let us assume 6 +√2 is rational.Then it can be expressed in the form p/q where p and q are co-prime.

Then,

```
6 +√2=p/q
```

√2 =p/q −6

√2 =(p −6q)/q -----( p,q,−6 are integers)

(p −6q) /q is rational

But, √2 is irrational.
This contradiction is due to our incorrect assumption that 6+√2 is rational.

Hence, 6 +√2 is irrational