# Math Help - Proving something is irrational

1. ## Proving something is irrational

Here's my problem...

Assume we know that √2 is irrational,

let x,y be any rational number such that y is not 0. Show that x + y√2 is irrational

Having a bit of trouble understanding proof and irrationals at uni

2. Originally Posted by lisa21a
Here's my problem...

Assume we know that √2 is irrational,

let x,y be any rational number such that y is not 0. Show that x + y√2 is irrational

Having a bit of trouble understanding proof and irrationals at uni
If $x+y\sqrt{2} = r$ where $x,y,r\in \mathbb{Q}$ then $\sqrt{2} = \tfrac{r-x}{y} \in \mathbb{Q}$.
This is impossible.