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 $2^{2}$.
$$\frac{2\times 2\sqrt{2}}{13\sqrt{12}}$$
Multiply $2$ and $2$ to get $4$.
$$\frac{4\sqrt{2}}{13\sqrt{12}}$$
Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$\frac{4\sqrt{2}}{13\times 2\sqrt{3}}$$
Multiply $13$ and $2$ to get $26$.
$$\frac{4\sqrt{2}}{26\sqrt{3}}$$
Cancel out $2$ in both numerator and denominator.
$$\frac{2\sqrt{2}}{13\sqrt{3}}$$
Rationalize the denominator of $\frac{2\sqrt{2}}{13\sqrt{3}}$ by multiplying numerator and denominator by $\sqrt{3}$.
