Lets draw a picture of the problem:
The magnitude of the sum will the the magnitude of the red vector. Since we have a right triangle, we can apply Pytagorean theorem, that is,
[tex]\begin{gathered} c^2=2^2+4^2 \\ c^2=4+16 \\ c^2=20 \end{gathered}[/tex]
Then, by applying square root to both sides, we have
[tex]\begin{gathered} c=\sqrt[]{20} \\ c=\sqrt[]{4\times5} \\ c=\sqrt[]{4}\times\sqrt[]{5} \end{gathered}[/tex]
Therefore, the answer is
[tex]c=2\sqrt[]{5}[/tex]
which correspondst to option 3 from left to right.
