Rewrite the square root of the division $\sqrt{\frac{64}{27}}$ as the division of square roots $\frac{\sqrt{64}}{\sqrt{27}}$.
$$\frac{\sqrt{64}}{\sqrt{27}}$$
Calculate the square root of $64$ and get $8$.
$$\frac{8}{\sqrt{27}}$$
Factor $27=3^{2}\times 3$. Rewrite the square root of the product $\sqrt{3^{2}\times 3}$ as the product of square roots $\sqrt{3^{2}}\sqrt{3}$. Take the square root of $3^{2}$.
$$\frac{8}{3\sqrt{3}}$$
Rationalize the denominator of $\frac{8}{3\sqrt{3}}$ by multiplying numerator and denominator by $\sqrt{3}$.
