Is the set $ \{(p_1,p_2,\dots, p_n):p_i\in \mathbb Q\}$ connected?

Question

Let $X=\{(p_1,p_2,\dots, p_n):p_i\in \mathbb Q\}$. Is $X $ connected or disconnected?

My attempt:$X$ is connected iff any two points of $X$ are contained in a connected subset of $X$. This attempt is Not working as it is difficult to find connected subsets of $X$. Would like to prove in this approach. Topology is usual topology of $\mathbb R^n$.

Answer 1

Hint: consider the hyperplanes $x_i=k$, ($i$ fixed, $k\in\Bbb R\setminus\Bbb Q$).