A Spiral for This Year

Calculus Level 4

Chong begins at his house and runs 2015 miles north, 2014 miles east, 2013 miles south, 2012 miles west, 2011 miles north... 2 miles east, and 1 mile south. What is the straight line distance from where he began to where he ended in miles?

If the answer can be represented by the form $$a\sqrt{b}$$, where $$a$$ and $$b$$ are positive integers and $$b$$ is squarefree, find $$ab$$.

Problem credit to my best friend William Asai

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