Answer
$$\dfrac{5\sqrt{14}}{7}$$
Work Step by Step
Simplify the radicand (expression inside the radical sign) by cancelling out the common factor $2$ to obtain:
\begin{align*}
\require{cancel}
&=\sqrt{\dfrac{\cancel{200}^{100}}{\cancel{28}^{14}}}\\\\
&=\sqrt{\dfrac{100}{14}}
\end{align*}
RECALL:
(1) For any real numbers $a \ge 0, b\ge0$, $\sqrt{ab}=\sqrt{a} \cdot \sqrt{b}$
(2) For any real numbers $a \ge 0, b\gt 0$, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$
Use rule (2) above to obtain:
\begin{align*}
\sqrt{\dfrac{100}{14}}&=\dfrac{\sqrt{100}}{\sqrt{14}}\\\\
&=\dfrac{10}{\sqrt{14}}
\end{align*}
Rationalize the denominator by multiplying $\sqrt{14}$ to both the numerator and denominator to obtain:
\begin{align*}
\dfrac{10}{\sqrt{14}} \cdot \dfrac{\sqrt{14}}{\sqrt{14}}&=\dfrac{10\sqrt{14}}{\sqrt{196}}\\\\
&=\dfrac{10\sqrt{14}}{14}
\end{align*}
Simplify by cancelling the common factor $2$ to obtain:
\begin{align*}
\require{cancel}
\dfrac{\cancel{10}^5\sqrt{14}}{\cancel{14}^7}&=\dfrac{5\sqrt{14}}{7}
\end{align*}
