order theory - $langle mathbb{R} times mathbb{R}, le_text{lex} rangle$ and $langle mathbb{R} times mathbb{Q}, le_text{lex} rangle$ are not isomorphic

Prove that ordered sets $\langle \mathbb{R} \times \mathbb{R}, \le_\text{lex} \rangle$ and $\langle \mathbb{R} \times \mathbb{Q}, \le_\text{lex} \rangle$ are not isomorphic ($\le_\text{lex}$ means lexicographical order).

I know that to prove that ordered sets are isomorphic, I would make a monotonic bijection, but how to prove they aren't isomorphic?