What's the shortest length here? Question: An ant starts at one vertex of a solid cube with side of unity length. Calculate
the distance of the shortest route the ant can take to the furthest vertex
from the starting point.

Now, in the answer, the cuboid is unfolded and a rectangle of side 1 and 2 is formed. Calculating the hyptoneuse gives the distance. 

That was the proposed solution. I wanted to calculate it via sqrt(1+1+1). Why is my answer wrong?
If you use $\sqrt{1+1+1}$, the answer is drilling straight through the cube.

What a talented ant. 

However, we need the ant to go in a path on the surface of a cube, which poses new challenges.

We can quickly visualize the ant going up the cube while going around to the other side.

This, as you mentioned is a straight line along the $1 \times 2$ rectangle formed by the path.

Therefore, the shortest length is $\sqrt{1^2+2^2}=\boxed{\sqrt{5}}$.
The distance from one corner to opposite corner of a 1x2 rectangle is $\sqrt{1^2+2^2}=\sqrt{5}$ and $\sqrt{5} \neq \sqrt{1+1+1} = \sqrt{3}$