Geneste wortel

$\begin{array}{l} \sqrt {2 - \sqrt 3 } = \sqrt a - \sqrt b \\ 2 - \sqrt 3 = a - 2\sqrt {ab} + b \\ \left\{ \begin{array}{l} a + b = 2 \\ 2\sqrt {ab} = \sqrt 3 \\ \end{array} \right. \\ \left\{ \begin{array}{l} a + b = 2 \\ 4ab = 3 \\ \end{array} \right. \\ \left\{ \begin{array}{l} a = 1\frac{1}{2} \\ b = \frac{1}{2} \\ \end{array} \right. \\ \sqrt {2 - \sqrt 3 } = \sqrt {1\frac{1}{2}} - \sqrt {\frac{1}{2}} \\ \sqrt {2 - \sqrt 3 } = \frac{1}{2}\sqrt 6 - \frac{1}{2}\sqrt 2 \\ \end{array}$