Why not write $\sqrt{3}2$? Is it just for aesthetic purposes, or is there a deeper reason why we write $2\sqrt{3}$ and not $\sqrt{3}2$?

The format $\sqrt{3}2$ is easliy confused with $\sqrt{32}$.
I also suspect that many early typesetters would skip the overline, so that $\sqrt{3}$ would be typeset as $\sqrt{\vphantom{3}}3$. In that case, $2\sqrt{\vphantom{3}}3$ is unambiguous but $\sqrt{\vphantom{3}}32$ highly ambiguous.
