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 $2^{2}$.
$$\frac{\sqrt{5}}{2\sqrt{2}}$$
Rationalize the denominator of $\frac{\sqrt{5}}{2\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
