\[\sqrt{\left( 5 - \sqrt{12} \right)^{2}} + \sqrt{\left( 3 - \sqrt{12} \right)^{2}} =\]
\[= \left| 5 - \sqrt{12} \right| + \left| 3 - \sqrt{12} \right| =\]
\[= 5 - \sqrt{12} + \sqrt{12} - 3 = 2.\]