Simplification of $\sqrt{14} - \sqrt{16 - 4 \sqrt{7}}$ I was trying to simplify $\sqrt{14} - \sqrt{16 - 4 \sqrt{7}}$. Numerical evaluation suggested that the answer is $\sqrt{2}$ and it checked out when I substituted $\sqrt{2}$ in the equation $x= \sqrt{14} - \sqrt{16 - 4 \sqrt{7}}$.
But I still cannot simplify the initial expression by any obvious means (squaring, multiplying by conjugate etc). Any idea how to do it? Can it be done?

\begin{align}
\Big(\sqrt{14} - \sqrt{16 - 4 \sqrt{7}}\Big)^2&=14+16-4\sqrt{7}-2\sqrt{14}\sqrt{16 - 4 \sqrt{7}}\\
&=30-4\sqrt{7}-4\sqrt{14}\sqrt{4 -  \sqrt{7}}\\
&=30-4\sqrt{7}-4\sqrt{56 -  14\sqrt{7}}\\
&=30-4\sqrt{7}-4\sqrt{49 -  2\times 7 \sqrt{7}+(\sqrt{7})^2}\\
&=30-4\sqrt{7}-4\sqrt{(7- \sqrt{7})^2}\\
&=30-4\sqrt{7}-4(7- \sqrt{7})\\
&=2
\end{align}
