Some treasure is hidden underground in a small square-shaped island of area $64 km^2$. You have no idea where the treasure is exactly, and no time to dig the whole island anyway.
But, luckily, you do have a very advanced device which can find any underground treasure in the area for a radius of 1 km.
You need to start somewhere and do the search. You can start up the device whenever you want on the island but you don't want anyone to interfere with your search, so you need to find a route which is as short as possible to cover the whole island.
So in the worst case scenario,
at least how many kilometers will it take to find the treasure on the island?
Note that; when you start to use the device, it is continously searching the area while you are moving.