Rewrite the square root of the division $\frac{1}{81}$ as the division of square roots $\frac{\sqrt{1}}{\sqrt{81}}$. Take the square root of both numerator and denominator.
$$\frac{3}{\frac{1}{9}}$$
Divide $3$ by $\frac{1}{9}$ by multiplying $3$ by the reciprocal of $\frac{1}{9}$.
