Answer
$3\sqrt{xy}$
Work Step by Step
The given expression can be written as:
$=\dfrac{1}{2}\cdot \dfrac{\sqrt{72xy}}{\sqrt{2}}$
RECALL:
(1) The quotient rule:
$\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$
where
$\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$
(2) $\dfrac{a^m}{a^n} = a^{m-n}, a \ne =0$
Use the quotient rule above to obtain:
$\require{cancel}=\dfrac{1}{2} \cdot \sqrt{\dfrac{72xy}{2}}
\\=\dfrac{1}{2} \cdot \sqrt{\dfrac{36\cancel{72}xy}{\cancel{2}}}
\\=\dfrac{1}{2} \cdot \sqrt{36xy}$
Factor the radicand so that at least one factor is a perfect square to obtain:
$=\dfrac{1}{2} \cdot \sqrt{36(xy)}
\\=\dfrac{1}{2} \cdot \sqrt{6^2(xy)}$
Simplify to obtain:
$=\frac{1}{2} \cdot 6\sqrt{xy}
\\=3\sqrt{xy}$
