Inverse Laplace transform of $\sqrt{H(s)}$

Question

In there any way to find inverse Laplace transform of a function in the following general form

\begin{equation} F(s)=\sqrt{\dfrac{a_n s^n+a_{n-1}s^{n-1}+\cdots+a_1 s+a_0}{b_n s^n+b_{n-1}s^{n-1}+\cdots+b_1 s+b_0}}. \end{equation}

For some very special cases, the answer is available in Laplace transform tables in term of the bessel functions.

Thanks,