Answer
$8.246\,m$.
Work Step by Step
We're given that $\vec{a} = (3\,m)\hat{i} + (4\,m)\hat{j}$ and $\vec{b} = (5\,m)\hat{i} + (-2\,m)\hat{j}$.
We can add these vectors component-wise;
$\vec{a}+\vec{b} = (3\,m+5\,m)\hat{i} + (4\,m-2\,m)\hat{j} = 8\,m\,\hat{i}+2\,m\,\hat{j}$.
The magnitude then equals (by Pythagorean's theorem):
$\sqrt{(8\,m)^2 + (2\,m)^2} = 8.246\,m$.
