Answer
$\dfrac{5\sqrt{xy}}{2}$
Work Step by Step
The given expression can be written as:
$=\dfrac{1}{2}\cdot \dfrac{\sqrt{50xy}}{\sqrt{2}}$
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:
$\require{cancel}=\dfrac{1}{2} \cdot \sqrt{\dfrac{50xy}{2}}
\\=\dfrac{1}{2} \cdot \sqrt{\dfrac{25\cancel{50}xy}{\cancel{2}}}
\\=\dfrac{1}{2} \cdot \sqrt{25xy}$
Factor the radicand so that at least one factor is a perfect square to obtain:
$=\dfrac{1}{2} \cdot \sqrt{25(xy)}
\\=\dfrac{1}{2} \cdot \sqrt{5^2(xy)}$
Simplify to obtain:
$=\frac{1}{2} \cdot 5\sqrt{xy}
\\=\dfrac{5\sqrt{xy}}{2}$
