\[\sqrt{\left( 4 - \sqrt{10} \right)^{2}} + \sqrt{\left( 3 - \sqrt{10} \right)^{2}} =\]
\[= \left| 4 - \sqrt{10} \right| + \left| 3 - \sqrt{10} \right| =\]
\[= 4 - \sqrt{10} + \sqrt{10} - 3 = 1.\]