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## Voorbeeld

$\begin{array}{l} \sqrt {5 + 2\sqrt 6 } = \sqrt a + \sqrt b \\ 5 + 2\sqrt 6 = a + 2\sqrt {ab} + b \\ 5 + 2\sqrt 6 = a + b + 2\sqrt {ab} \\ \left\{ \begin{array}{l} a + b = 5 \\ ab = 6 \\ \end{array} \right. \\ \left\{ \begin{array}{l} a + b = 5 \\ a = \frac{6}{b} \\ \end{array} \right. \\ \left\{ \begin{array}{l} \frac{6}{b} + b = 5 \\ a = \frac{6}{b} \\ \end{array} \right. \\ \left\{ \begin{array}{l} 6 + b^2 = 5b \\ a = \frac{6}{b} \\ \end{array} \right. \\ \left\{ \begin{array}{l} b^2 - 5b + 6 = 0 \\ a = \frac{6}{b} \\ \end{array} \right. \\ \left\{ \begin{array}{l} \left( {b - 2} \right)\left( {b - 3} \right) = 0 \\ a = \frac{6}{b} \\ \end{array} \right. \\ \left\{ \begin{array}{l} b = 2 \vee b = 3 \\ a = \frac{6}{b} \\ \end{array} \right. \\ \left\{ \begin{array}{l} b = 2 \\ a = 3 \\ \end{array} \right. \vee \left\{ \begin{array}{l} b = 3 \\ a = 2 \\ \end{array} \right. \\ \sqrt {5 + 2\sqrt 6 } = \sqrt 2 + \sqrt 3 \\ \end{array}$

Met de formule!?

$\begin{array}{l} \sqrt {5 + 2\sqrt 6 } = a + b\sqrt c \\ a = \sqrt 2 \\ b = \frac{1}{2}\sqrt 2 \\ c = 6 \\ \sqrt {5 + 2\sqrt 6 } = \sqrt 2 + \frac{1}{2}\sqrt 2 \sqrt 6 = \sqrt 2 + \sqrt 3 \\ \end{array}$