Since we have two different answers I might as well do it as well
$$\\x=\sqrt{(\sqrt{15}-\sqrt{3})^2+(\sqrt{15}-\sqrt{3})^2}\\\\
x=\sqrt{2*(15-2\sqrt{45}+3)}\\\\
x=\sqrt{2*(18-6\sqrt{5})}\\\\
x=\sqrt{36-12\sqrt{5}}\\\\$$
$${\sqrt{{\mathtt{36}}{\mathtt{\,-\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}}} = {\mathtt{3.027\: \!735\: \!832\: \!268\: \!483\: \!3}}$$
check
$${\sqrt{{\mathtt{2}}{\mathtt{\,\times\,}}{\left({\sqrt{{\mathtt{15}}}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{3}}}}\right)}^{{\mathtt{2}}}}} = {\mathtt{3.027\: \!735\: \!832\: \!268\: \!483\: \!3}}$$
Seems anon is correct on this one.
Sorry Chris. 