# Random Points On A Square

Calculus Level 5

A square with a unit length has two arbitrary points chosen inside it. What is the average distance between the two points?

If this can be represented in the form $$\dfrac {a + \sqrt{b} + c \ln (d+\sqrt{e})}{f}$$, where $$a, b, c, d, e, f$$ are positive integers, and the fraction is simplified as far as possible, find $$a+b+c+d+e+f$$.

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