Think logically not mathematically[part-13]

the largest size of a cube is its diagonal therefore the largest size of the stick is $\sqrt{3}\times1.732=\sqrt{3}\times\sqrt{3}=(\sqrt{3})^2=3$

I did it this way. Say we have at the bottom left corner of the cube as the origin of the Cartesian coordinate system. Now, given that all sides are $\sqrt{3}$ units in length. Let's consider a vector that points from the origin (the bottom left corner of the cube) to the top right corner(diagonally):
$v = \sqrt{3}i + \sqrt{3}j + \sqrt{3}k$
which is the required stick. For the maximum length, all we need to do is to determine the length of this vector. Therefore, $||v|| = \sqrt{ (\sqrt{3})^{2} + (\sqrt{3})^{2} + (\sqrt{3})^{2}} = \sqrt{3 + 3 + 3} = \boxed{3}$ .