# This Spiral is So Radical Dude!

Calculus Level 4

A particle begins at the origin and moves lengths of $$\frac{1}{\sqrt1+\sqrt5}$$ units east, $$\frac{1}{\sqrt2+\sqrt6}$$ units north, $$\frac{1}{\sqrt3+\sqrt7}$$ units west, $$\frac{1}{\sqrt4+\sqrt8}$$ units south... ad infinitum.

If the magnitude of the displacement of the particle from the origin is $$P$$, enter your answer as $$\lfloor 1000P\rfloor$$.

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