Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
M = \left( {\sqrt 2 - \sqrt {3 - \sqrt 5 } } \right).\sqrt 2 + \sqrt {20} \\
= \sqrt 2 .\sqrt 2 - \sqrt {3 - \sqrt 5 } .\sqrt 2 + \sqrt {20} \\
= 2 - \sqrt {2.\left( {3 - \sqrt 5 } \right)} + \sqrt {{2^2}.5} \\
= 2 - \sqrt {6 - 2\sqrt 5 } + 2\sqrt 5 \\
= 2 - \sqrt {5 - 2.\sqrt 5 .1 + 1} + 2\sqrt 5 \\
= 2 - \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} + 2\sqrt 5 \\
= 2 - \left( {\sqrt 5 - 1} \right) + 2\sqrt 5 \\
= \sqrt 5 + 3\\
b,\\
N = \left( {\dfrac{{\sqrt 6 - \sqrt 2 }}{{1 - \sqrt 3 }} - \dfrac{5}{{\sqrt 5 }}} \right):\dfrac{1}{{\sqrt 5 - \sqrt 2 }}\\
= \left( {\dfrac{{\sqrt 2 .\left( {\sqrt 3 - 1} \right)}}{{1 - \sqrt 3 }} - \dfrac{{{{\sqrt 5 }^2}}}{{\sqrt 5 }}} \right).\left( {\sqrt 5 - \sqrt 2 } \right)\\
= \left( { - \sqrt 2 - \sqrt 5 } \right).\left( {\sqrt 5 - \sqrt 2 } \right)\\
= - \left( {\sqrt 5 + \sqrt 2 } \right).\left( {\sqrt 5 - \sqrt 2 } \right)\\
= - \left( {5 - 2} \right)\\
= - 3
\end{array}\)
