$\begin{array}{l} 12)\sqrt {5 - 2\sqrt {7 - 2\sqrt 6 } } \\ = \sqrt {5 - 2\sqrt {{{\left( {\sqrt 6 - 1} \right)}^2}} } \\ = \sqrt {5 - 2\left( {\sqrt 6 - 1} \right)} = \sqrt {7 - 2\sqrt 6 } \\ = \sqrt {{{\left( {\sqrt 7 - 1} \right)}^2}} = \sqrt 7 - 1\\ 13)\sqrt {8 - 2\sqrt 7 } = \sqrt {7 + 1 - 2.1.\sqrt 7 } = \sqrt {{{\left( {\sqrt 7 - 1} \right)}^2}} = \sqrt 7 - 1\\ 14)\sqrt {6 + 2\sqrt 5 } - \sqrt {6 - 2\sqrt 5 } = \sqrt {5 + 1 + 2.1.\sqrt 5 } - \sqrt {5 + 1 - 2.1\sqrt 5 } \\ = \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\ = \sqrt 5 + 1 - \sqrt 5 + 1 = 2 \end{array}$
