Giải thích các bước giải:
\(\begin{array}{l}
a.\frac{{\sqrt 5 \left( {1 - \sqrt 3 } \right)}}{{1 - \sqrt 3 }} - \sqrt {{{\left( {2\sqrt 5 } \right)}^2} + 2.2\sqrt 5 .1 + 1} \\
= \sqrt 5 - \sqrt {{{\left( {2\sqrt 5 + 1} \right)}^2}} = \sqrt 5 - \left( {2\sqrt 5 + 1} \right) = - 1 - \sqrt 5 \\
b.3\sqrt {50} - 2\sqrt {98} - 5\sqrt {18} - \sqrt {63} + 2\sqrt {28} \\
= 15\sqrt 2 - 14\sqrt 2 - 15\sqrt 2 - 3\sqrt 7 + 4\sqrt 7 \\
= - 14\sqrt 2 + \sqrt 7 \\
c.\frac{4}{{\sqrt 7 - \sqrt 3 }} + \frac{{2\sqrt 3 .\sqrt 3 }}{{\sqrt 3 \left( {\sqrt 3 + 1} \right)}} + \frac{{\sqrt 7 \left( {1 - \sqrt 7 } \right)}}{{\sqrt 7 - 1}}\\
= \frac{4}{{\sqrt 7 - \sqrt 3 }} + \frac{{2\sqrt 3 }}{{\sqrt 3 + 1}} - \sqrt 7 \\
= \frac{{4\sqrt 3 + 4 + 2\sqrt {21} - 6 - \left( {7 - \sqrt {21} } \right)\left( {\sqrt 3 + 1} \right)}}{{\left( {\sqrt 7 - \sqrt 3 } \right)\left( {\sqrt 3 + 1} \right)}}\\
= \frac{{4\sqrt 3 + 2\sqrt {21} - 2 - 7\sqrt 3 - 7 + 3\sqrt 7 + \sqrt {21} }}{{\left( {\sqrt 7 - \sqrt 3 } \right)\left( {\sqrt 3 + 1} \right)}}\\
= \frac{{3\sqrt {21} - 3\sqrt 3 + 3\sqrt 7 - 9}}{{\left( {\sqrt 7 - \sqrt 3 } \right)\left( {\sqrt 3 + 1} \right)}}\\
= \frac{{3\sqrt 7 \left( {\sqrt 3 + 1} \right) - 3\sqrt 3 \left( {1 + \sqrt 3 } \right)}}{{\left( {\sqrt 7 - \sqrt 3 } \right)\left( {\sqrt 3 + 1} \right)}}\\
= \frac{{\left( {\sqrt 3 + 1} \right)\left( {3\sqrt 7 - 3\sqrt 3 } \right)}}{{\left( {\sqrt 7 - \sqrt 3 } \right)\left( {\sqrt 3 + 1} \right)}} = 3\\
d.\sqrt {5 - 2.2.\sqrt 5 + 4} - \frac{2}{{\sqrt 5 - 1}}\\
= \sqrt {{{\left( {\sqrt 5 - 2} \right)}^2}} - \frac{2}{{\sqrt 5 - 1}}\\
= \sqrt 5 - 2 - \frac{2}{{\sqrt 5 - 1}}\\
= \frac{{5 - \sqrt 5 - 2\sqrt 5 + 2 - 2}}{{\sqrt 5 - 1}}\\
= \frac{{5 - 3\sqrt 5 }}{{\sqrt 5 - 1}}
\end{array}\)
