Question 99
For a positive integer $n$ it is known that the number $\sqrt{12n^2 + 1}$ also is a positive integer. Prove that the number
$$
\sqrt{\frac{\sqrt{12n^2 + 1} + 1}{2}}
$$
also is a positive integer.
$$
\sqrt{\frac{\sqrt{12n^2 + 1} + 1}{2}}
$$
also is a positive integer.