Giải thích các bước giải:
\(\begin{array}{l}
H = \sqrt {\frac{{2\sqrt {10} + \sqrt {30} - 2\sqrt 2 - \sqrt 6 }}{{2\sqrt {10} - 2\sqrt 2 }}} :\frac{2}{{\sqrt 3 - 1}}\\
H = \sqrt {\frac{{2\sqrt 2 .\sqrt 5 + \sqrt 5 .\sqrt 6 - 2\sqrt 2 - \sqrt 6 }}{{2\sqrt 2 .\sqrt 5 - 2\sqrt 2 }}} \times \frac{{\sqrt 3 - 1}}{2}\\
H = \sqrt {\frac{{\left( {2\sqrt 2 + \sqrt 6 } \right).\sqrt 5 - \left( {2\sqrt 2 + \sqrt 6 } \right)}}{{2\sqrt 2 .\left( {\sqrt 5 - 1} \right)}}} \times \frac{{\sqrt 3 - 1}}{2}\\
H = \sqrt {\frac{{\left( {2\sqrt 2 + \sqrt 6 } \right).\left( {\sqrt 5 - 1} \right)}}{{2\sqrt 2 .\left( {\sqrt 5 - 1} \right)}}} \times \frac{{\sqrt 3 - 1}}{2}\\
H = \sqrt {\frac{{2\sqrt 2 + \sqrt 2 .\sqrt 3 }}{{2\sqrt 2 }}} \times \frac{{\sqrt 3 - 1}}{2}\\
H = \sqrt {\frac{{\sqrt 2 \left( {2 + \sqrt 3 } \right)}}{{2\sqrt 2 }}} \times \frac{{\sqrt 3 - 1}}{2}\\
H = \sqrt {\frac{{2 + \sqrt 3 }}{2} \times {{\left( {\frac{{\sqrt 3 - 1}}{2}} \right)}^2}} \\
H = \sqrt {\frac{{\left( {2 + \sqrt 3 } \right){{\left( {\sqrt 3 - 1} \right)}^2}}}{{2.4}}} \\
H = \sqrt {\frac{{\left( {2 + \sqrt 3 } \right)\left( {3 - 2\sqrt 3 + 1} \right)}}{8}} \\
H = \sqrt {\frac{{6 - 4\sqrt 3 + 2 + 3\sqrt 3 - 6 + \sqrt 3 }}{8}} \\
H = \sqrt {\frac{1}{4}} = \frac{1}{2}
\end{array}\)
