解：$(1) $原式$=\sqrt {3×2÷30}$
$=\sqrt {\frac {6}{30}}$
$=\sqrt {\frac {1}{5}}$
$=\frac {\sqrt {5}}{5}$
$ (2) $原式$=2\sqrt {\frac {3}{2}}÷5\sqrt {\frac {1}{6}}×\sqrt {12}$
$ =\frac {2}{5}×\sqrt {\frac {3}{2}÷\frac {1}{6}×12}$
$ =\frac {2}{5}×\sqrt {108}$
$ =\frac {2}{5}×6\sqrt {3}$
$=\frac {12\sqrt {3}}{5}$
$ (3) $原式$=\sqrt {18}÷(3\sqrt {2}×2\sqrt {2})$
$=3\sqrt {2}÷12$
$=\frac {\sqrt {2}}{4}$
$ (4) $原式$=\sqrt {6x^2÷24x}$
$=\sqrt {\frac {x}{4}}$
$=\frac {\sqrt {x}}{2}$
