\(\begin{align}
  & 4 \\
& =\sqrt{16} \\
& =\sqrt{6+10} \\
& =\sqrt{6+2\sqrt{25}} \\
& =\sqrt{6+2\sqrt{7+18}} \\
& =\sqrt{6+2\sqrt{7+3\sqrt{36}}} \\
& =\sqrt{6+2\sqrt{7+3\sqrt{8+28}}} \\
& =\sqrt{6+2\sqrt{7+3\sqrt{8+4\sqrt{49}}}} \\
& =\sqrt{6+2\sqrt{7+3\sqrt{8+4\sqrt{9+\cdots }}}} \\
\end{align}\)

計算題的話，可用數學歸納法證明
\(\sqrt{\left( n+1 \right)+\left( n-3 \right)\sqrt{\left( n+2 \right)+\left( n-2 \right)\sqrt{\left( n+3 \right)+\left( n-1 \right)\sqrt{\left( n+4 \right)+\cdots }}}}=n-1\)