Answer
$\sqrt{34}+\sqrt{13}.$
Work Step by Step
We know that if $k=ai+bj$ and $l=ci+dj$, then $k+l=(a+c)i+(b+d)j$ and that if $z$ is a constant, then $zk=(za)i+(zb)j$.
Also, the magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$.
Hence here: $||v||+||w||=||(3i-5j)||+||(-2i+3j)||=\sqrt{3^2+(-5)^2}+\sqrt{(-2)^2+3^2}=\sqrt{9+25}+\sqrt{4+9}=\sqrt{34}+\sqrt{13}.$
