# Merasionalkan Bentuk Akar

## Konsep Dasar

Contoh 1:

\begin{equation*}
\begin{split}
& \frac{1}{\sqrt{2}} \quad {\color {blue} \times \frac{\sqrt{2}}{\sqrt{2}}}  \\\\
& \frac{\sqrt{2}}{2} \\\\
& \frac{1}{2} \sqrt{2}
\end{split}
\end{equation*}

Contoh 2:

\begin{equation*}
\begin{split}
& \frac{1}{\sqrt{5} + \sqrt{2}} \quad {\color {blue} \times \frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}}  \\\\
& \frac{\sqrt{5} - \sqrt{2}}{(\sqrt{5})^2 - (\sqrt{2})^2} \quad {\color {blue} (a + b)(a - b) = a^2 - b^2} \\\\
& \frac{\sqrt{5} - \sqrt{2}}{5 - 2} \\\\
& \frac{\sqrt{5} - \sqrt{2}}{3} \\\\
& \frac{1}{3} (\sqrt{5} - \sqrt{2})
\end{split}
\end{equation*}

Contoh 3:

\begin{equation*}
\begin{split}
& \frac{20}{\sqrt{2} + \sqrt{7} + \sqrt{5}} \quad {\color {blue} \text{angka paling besar dipisahkan: } \sqrt{7}}  \\\\
& \frac{20}{(\sqrt{2} + \sqrt{5}) + \sqrt{7}} \quad {\color {blue} \times \frac{(\sqrt{2} + \sqrt{5}) - \sqrt{7}}{(\sqrt{2} + \sqrt{5}) - \sqrt{7}} } \\\\
& \frac{20(\sqrt{2} + \sqrt{5} - \sqrt{7})}{(\sqrt{2} + \sqrt{5})^2 - (\sqrt{7})^2} \quad {\color {blue} (a + b)(a - b) = a^2 - b^2} \\\\
& \frac{20(\sqrt{2} + \sqrt{5} - \sqrt{7})}{2 + 2\sqrt{10} + 5 - 7} \quad {\color {blue} (a + b)^2 = a^2 + 2ab + b^2} \\\\
& \frac{20(\sqrt{2} + \sqrt{5} - \sqrt{7})}{2\sqrt{10}} \\\\
& \frac{20(\sqrt{2} + \sqrt{5} - \sqrt{7})}{2\sqrt{10}} \quad{ \color {blue} \times \frac{\sqrt{10}}{\sqrt{10}}}\\\\
& \frac{20(\sqrt{20} + \sqrt{50} - \sqrt{70})}{20} \\\\
& \sqrt{20} + \sqrt{50} - \sqrt{70} \\\\
& 2\sqrt{5} + 5\sqrt{2} - \sqrt{70}
\end{split}
\end{equation*}