An elf finds himself in a random place in a square field that is \(2\text{ km}\) by \(2 \text{ km} \). Right in the centre of the field is the present factory, which can be assumed to be a point.

###### This problem is part of the Advent Calendar 2015.

He needs to return to the factory promptly, so he does so by walking in a straight line back to the factory (the shortest distance).

Find the **root mean square** average of the length of his journey, and give your answer **to the nearest metre**.

**Note**: The root mean square is also known as the *quadratic mean*.

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