Multiply $0.00108$ and $10000000000000$ to get $10800000000$.
$$\sqrt{\frac{0.003888}{10800000000}}$$
Expand $\frac{0.003888}{10800000000}$ by multiplying both numerator and the denominator by $1000000$.
$$\sqrt{\frac{3888}{10800000000000000}}$$
Reduce the fraction $\frac{3888}{10800000000000000}$ to lowest terms by extracting and canceling out $432$.
$$\sqrt{\frac{9}{25000000000000}}$$
Rewrite the square root of the division $\frac{9}{25000000000000}$ as the division of square roots $\frac{\sqrt{9}}{\sqrt{25000000000000}}$. Take the square root of both numerator and denominator.