Inspired by Pi Han Goh

Algebra Level pending

Note that \( \sqrt{79} - 8 \approx 0.888 \) and \(\sqrt{320} - 17\approx 0.888\) in the sense that the first 3 decimal places of these two numbers are equal.

Now we see that \(\lfloor 1000 (\sqrt{79} - 8) \rfloor =\lfloor 1000 (\sqrt{320} - 17) \rfloor = 888\).

Suppose \( \lfloor 1000 (\sqrt{x} - y) \rfloor =888 \) where \(x, y\) are positive integers and \(x>320\). What is the minimum value of \(x+y\)?


Inspiration.

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