$\displaystyle \begin{array}{{>{\displaystyle}l}} \sqrt{7-\sqrt{6}} -\sqrt{7+\sqrt{6} \ } =A\\ A^{2} =7-\sqrt{6} +7+\sqrt{6} +2\sqrt{\left( 7-\sqrt{6}\right)\left( 7+\sqrt{6}\right)} \ \\ A^{2} =14+2\sqrt{43} \ \\ \rightarrow A=\sqrt{14+2\sqrt{43}}\\ \\ \\ \end{array}$
