\(\sqrt{(a + b) + 2 \sqrt{ab}} = \sqrt{a} + \sqrt{b}\)
\(\sqrt{(a + b) - 2 \sqrt{ab}} = \sqrt{a} - \sqrt{b}\)
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*}
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*}