$$\eqalign{
{\text{Упростите:}} \hfill \\
\sqrt {2 + \sqrt 3 } + \sqrt {2 - \sqrt 3 } . \hfill \\
} $$
$$\eqalign{
A = \sqrt {2 + \sqrt 3 } + \sqrt {2 - \sqrt 3 } . \hfill \\
{A^2} = {\left( {\sqrt {2 + \sqrt 3 } + \sqrt {2 - \sqrt 3 } } \right)^2} = 2 + \sqrt 3 + 2\sqrt {2 + \sqrt 3 } \sqrt {2 - \sqrt 3 } + 2 - \sqrt 3 = \hfill \\
4 + 2\sqrt {\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)} = 4 + 2\sqrt 1 = 6 \Rightarrow A = \sqrt 6 . \hfill \\
} $$
\[\sqrt 6 \]
