Write two rational numbers between $\sqrt{2} \text{ and } \sqrt{3}$.

We want two rational numbers between $\sqrt{2} \text{ and } \sqrt{3}$.

Consider any two rational numbers between 2 and 3 such that they are perfect squares.

Let us take 2.25 and 2.56, such that $\sqrt{2.25} = 1.5 \text{ and } \sqrt{2.56} = 1.6$.

Thus, we have :

$\Rightarrow \sqrt{2} \lt 1.5 \lt 1.6 \lt \sqrt{3}$

Hence, two rational numbers between $\sqrt{2} \text{ and } \sqrt{3}$ are 1.5 and 1.6