Answer
$$\sqrt {221} $$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{u}} = \left\langle {2,4, - 5} \right\rangle {\text{ and }}{\bf{v}} = \left\langle { - 6,10,2} \right\rangle \cr
& {\bf{u}} + {\bf{v}} = \left\langle {2,4, - 5} \right\rangle + \left\langle { - 6,10,2} \right\rangle \cr
& {\text{Add the vectors}} \cr
& {\bf{u}} + {\bf{v}} = \left\langle {2 - 6,4 + 10, - 5 + 2} \right\rangle \cr
& {\bf{u}} + {\bf{v}} = \left\langle { - 4,14, - 3} \right\rangle \cr
& {\text{Calculate }}\left| {{\bf{u}} + {\bf{v}}} \right| \cr
& \left| {{\bf{u}} + {\bf{v}}} \right| = \left| {\left\langle { - 4,14, - 3} \right\rangle } \right| \cr
& \left| {{\bf{u}} + {\bf{v}}} \right| = \sqrt {{{\left( { - 4} \right)}^2} + {{\left( {14} \right)}^2} + {{\left( { - 3} \right)}^2}} \cr
& \left| {{\bf{u}} + {\bf{v}}} \right| = \sqrt {16 + 196 + 9} \cr
& \left| {{\bf{u}} + {\bf{v}}} \right| = \sqrt {221} \cr} $$
