Factor $568=2^{2}\times 142$. Rewrite the square root of the product $\sqrt{2^{2}\times 142}$ as the product of square roots $\sqrt{2^{2}}\sqrt{142}$. Take the square root of $2^{2}$.
$$\frac{9}{2\sqrt{142}}$$
Rationalize the denominator of $\frac{9}{2\sqrt{142}}$ by multiplying numerator and denominator by $\sqrt{142}$.
