Rewrite the square root of the division $\frac{1}{4}$ as the division of square roots $\frac{\sqrt{1}}{\sqrt{4}}$. Take the square root of both numerator and denominator.
$$\frac{\frac{1}{2}}{\sqrt{\frac{324}{81}}}$$
Divide $324$ by $81$ to get $4$.
$$\frac{\frac{1}{2}}{\sqrt{4}}$$
Calculate the square root of $4$ and get $2$.
$$\frac{\frac{1}{2}}{2}$$
Express $\frac{\frac{1}{2}}{2}$ as a single fraction.
