Bentuk Akar di Dalam Akar

Pembuktian

\begin{equation*}
\begin{split}
(a + b)^2 & = a^2 + 2ab + b^2 \\\\
(\sqrt{a} + \sqrt{b})^2 & = a + 2 \sqrt{a} \sqrt{b} + b \\\\
(\sqrt{a} + \sqrt{b})^2 & = a + b + 2 \sqrt{ab} \\\\
\sqrt{a} + \sqrt{b} & = \sqrt{a + b + 2 \sqrt{ab}}
\end{split}
\end{equation*}

\begin{equation*}
\begin{split}
(a - b)^2 & = a^2 - 2ab + b^2 \\\\
(\sqrt{a} - \sqrt{b})^2 & = a - 2 \sqrt{a} \sqrt{b} + b \\\\
(\sqrt{a} - \sqrt{b})^2 & = a + b - 2 \sqrt{ab} \\\\
\sqrt{a} - \sqrt{b} & = \sqrt{a + b - 2 \sqrt{ab}}
\end{split}
\end{equation*}