Find two rational numbers between $2\sqrt{3}$ and $\sqrt{15}$.

$2\sqrt{3}$ = $\sqrt{4 × 3}$ = $\sqrt{12}$

So, we need to find two irrational number between $\sqrt{12}$ and $\sqrt{15}$

$\text{Since}, 12 \lt 12.25 \lt 12.96 \lt 15 \\[0.5em] \Rightarrow \sqrt{12} \lt \sqrt{12.25} \lt \sqrt{12.96} \lt \sqrt{15}$

Hence, two rational number between $\sqrt{12}$ and $\sqrt{15}$ are $\bold{\sqrt{12.25}}$ and $\bold{\sqrt{12.96}}$ .