Precalculus (10th Edition)

$\sqrt{5}+5$
The magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$. Hence, $||v||=\sqrt{(-2)^2+1^2}\\ ||v||=\sqrt{4+1}\\ ||v||=\sqrt{5}$ $||w||=\sqrt{4^2+(-3)^2}\\ ||w||=\sqrt{16+9}\\ ||w||=\sqrt{25}\\ ||w||=5$ Thus, $||v||+||w||=\sqrt{5}+5$