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Nested Square Roots (Posted on 2025-02-07)

For how many positive integers n is √(n + √(n + √(n + √n))) an integer?

No Solution Yet Submitted by Danish Ahmed Khan

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Solution?

| Comment 1 of 4

n=0 is a solution.

If n is not a perfect square, it's easy to see the result is irrational.

If n=a^2, then the right most nested term is sqrt(a^2+a) , which is not an integer and therefore irrational.

Posted by Kenny M on 2025-02-08 22:22:49

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