Is the set $\{ x\in \mathbb{Q}: 2< x^2

Is the set $\{ x\in \mathbb{Q}: 2< x^2 <3\}$ closed, bounded, compact in $\mathbb{Q}$ ?

I think $\{ x\in \mathbb{Q}: 2< x^2 <3\}=\{ x\in \mathbb{Q}: 2\leq x^2 \leq 3\}$, so it is bounded and closed in $Q$, is that right?