Factor $18=3^{2}\times 2$. Rewrite the square root of the product $\sqrt{3^{2}\times 2}$ as the product of square roots $\sqrt{3^{2}}\sqrt{2}$. Take the square root of $3^{2}$.
$$\sqrt{\frac{12\sqrt{2}}{5\times 3\sqrt{2}}}$$
Multiply $5$ and $3$ to get $15$.
$$\sqrt{\frac{12\sqrt{2}}{15\sqrt{2}}}$$
Cancel out $3\sqrt{2}$ in both numerator and denominator.
$$\sqrt{\frac{4}{5}}$$
Rewrite the square root of the division $\sqrt{\frac{4}{5}}$ as the division of square roots $\frac{\sqrt{4}}{\sqrt{5}}$.
$$\frac{\sqrt{4}}{\sqrt{5}}$$
Calculate the square root of $4$ and get $2$.
$$\frac{2}{\sqrt{5}}$$
Rationalize the denominator of $\frac{2}{\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.
