It can be shown that for any positive integer n, the infinitely nested radical expression

(n+(n+(n+....)^1/2)^1/2)^1/2
equals a finite number. What is the largest positive integer n≤999 such that this expression is equal to a positive integer?

Details and assumptions
A nested radical expression is one which contains a radical inside another one, as in
((5^1/2)+3)^1/2

An infinitely nested radical expression is one in which the radicals continue to an infinite extent.

4 answers

SO WHAT'S the Correct Answer ??

991

991 us wrong !!!

992

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