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 $\displaystyle x+y\sqrt{2} = r$ where $\displaystyle x,y,r\in \mathbb{Q}$ then $\displaystyle \sqrt{2} = \tfrac{r-x}{y} \in \mathbb{Q}$.
This is impossible.