Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$\frac{3}{2\times 2\sqrt{2}}$$
Multiply $2$ and $2$ to get $4$.
$$\frac{3}{4\sqrt{2}}$$
Rationalize the denominator of $\frac{3}{4\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
