Đáp án:
$\begin{array}{l}
a)\sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} - \sqrt 3 \\
= 2 + \sqrt 3 - \sqrt 3 \\
= 2\\
b)\dfrac{{x\sqrt y + y\sqrt x }}{{\sqrt {xy} }}:\dfrac{1}{{\sqrt x - \sqrt y }}\\
= \dfrac{{\sqrt {xy} \left( {\sqrt x + \sqrt y } \right)}}{{\sqrt {xy} }}.\left( {\sqrt x - \sqrt y } \right)\\
= \left( {\sqrt x + \sqrt y } \right)\left( {\sqrt x - \sqrt y } \right)\\
= x - y
\end{array}$