Đáp án:
$\begin{array}{l}
a)\sqrt {\dfrac{1}{{x - 1}}} = \dfrac{{\sqrt {x - 1} }}{{x - 1}}\\
b)\sqrt {\dfrac{{x - y}}{{x + y}}} = \dfrac{{\sqrt {x - y} \sqrt {x + y} }}{{x + y}} = \dfrac{{\sqrt {{x^2} - {y^2}} }}{{x + y}}\\
c)\sqrt {\dfrac{{{{\left( {x - 3} \right)}^2}}}{{627}}} \left( {x > 3} \right)\\
= \dfrac{{x - 3}}{{\sqrt {627} }} = \dfrac{{\sqrt {627} \left( {x - 3} \right)}}{{627}}\\
d)\sqrt {\dfrac{{x\sqrt y - y\sqrt x }}{{\sqrt {xy} \left( {\sqrt x + \sqrt y } \right)}}} \\
= \sqrt {\dfrac{{\sqrt {xy} \left( {\sqrt x - \sqrt y } \right)}}{{\sqrt {xy} \left( {\sqrt x + \sqrt y } \right)}}} \\
= \sqrt {\dfrac{{\sqrt x - \sqrt y }}{{\sqrt x + \sqrt y }}} \\
= \dfrac{{\sqrt {{{\left( {\sqrt x - \sqrt y } \right)}^2}} }}{{\sqrt {x - y} }}\\
= \dfrac{{\left( {\sqrt x - \sqrt y } \right).\sqrt {x - y} }}{{x - y}}
\end{array}$
