Toepassing
$
\large\begin{array}{l}
\sqrt {\frac{{1143}}{{32}} + \frac{{105}}{{32}}\sqrt {65} } = ? \\
a = \frac{1}{2}\sqrt 2 \sqrt {\frac{{1143}}{{32}} - \sqrt {\left( {\frac{{1143}}{{32}}} \right)^2 - \left( {\frac{{105}}{{32}}} \right)^2 \cdot 65}} = \frac{5}{8}\sqrt {15} \\
b = \frac{{\frac{{105}}{{32}}\sqrt 2 }}{2{\sqrt {\frac{{1143}}{{32}} - \sqrt {\left( {\frac{{1143}}{{32}}} \right)^2 - \left( {\frac{{105}}{{32}}} \right)^2 \cdot 65} }}} = \frac{7}{{40}}\sqrt {15} \\
c = 65 \\
\sqrt {\frac{{1143}}{{32}} + \frac{{105}}{{32}}\sqrt {65} } = \frac{5}{8}\sqrt {15} + \frac{7}{{40}}\sqrt {15} \cdot \sqrt {65} = \frac{5}{8}\sqrt {15} + \frac{7}{8}\sqrt {39} \\
\end{array}$