Giải thích các bước giải:
$\begin{array}{l}
a)A = \sqrt {9 + 4\sqrt 5 } + \sqrt {9 - 4\sqrt 5 } \\
= \sqrt {5 + 4\sqrt 5 + 4} + \sqrt {5 - 4\sqrt 5 + 4} \\
= \sqrt {{{\left( {\sqrt 5 + 2} \right)}^2}} + \sqrt {{{\left( {\sqrt 5 - 2} \right)}^2}} \\
= \left| {\sqrt 5 + 2} \right| + \left| {\sqrt 5 - 2} \right|\\
= \sqrt 5 + 2 + \sqrt 5 - 2\\
= 2\sqrt 5 \\
b)B = \dfrac{1}{{\sqrt 3 - \sqrt 5 }} + \dfrac{1}{{\sqrt 3 + \sqrt 5 }}\\
= \dfrac{{\sqrt 3 + \sqrt 5 + \sqrt 3 - \sqrt 5 }}{{\left( {\sqrt 3 - \sqrt 5 } \right)\left( {\sqrt 3 + \sqrt 5 } \right)}}\\
= \dfrac{{2\sqrt 3 }}{{{{\left( {\sqrt 3 } \right)}^2} - {{\left( {\sqrt 5 } \right)}^2}}}\\
= \dfrac{{2\sqrt 3 }}{{ - 2}}\\
= - \sqrt 3 \\
c)C = \dfrac{1}{{\sqrt 2 + \sqrt 3 }} + \dfrac{1}{{\sqrt 3 + \sqrt 4 }} + \dfrac{1}{{\sqrt 4 + \sqrt 5 }}\\
= \dfrac{{\sqrt 3 - \sqrt 2 }}{{\left( {\sqrt 2 + \sqrt 3 } \right)\left( {\sqrt 3 - \sqrt 2 } \right)}} + \dfrac{{\sqrt 4 - \sqrt 3 }}{{\left( {\sqrt 3 + \sqrt 4 } \right)\left( {\sqrt 4 - \sqrt 3 } \right)}} + \dfrac{{\sqrt 5 - \sqrt 4 }}{{\left( {\sqrt 5 + \sqrt 4 } \right)\left( {\sqrt 5 - \sqrt 4 } \right)}}\\
= \dfrac{{\sqrt 3 - \sqrt 2 }}{1} + \dfrac{{\sqrt 4 - \sqrt 3 }}{1} + \dfrac{{\sqrt 5 - \sqrt 4 }}{1}\\
= \sqrt 5 - \sqrt 2
\end{array}$
