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 $3^{2}$.
Factor $20=2^{2}\times 5$. Rewrite the square root of the product $\sqrt{2^{2}\times 5}$ as the product of square roots $\sqrt{2^{2}}\sqrt{5}$. Take the square root of $2^{2}$.
Factor $24=2^{2}\times 6$. Rewrite the square root of the product $\sqrt{2^{2}\times 6}$ as the product of square roots $\sqrt{2^{2}}\sqrt{6}$. Take the square root of $2^{2}$.
To multiply $\sqrt{2}$ and $\sqrt{5}$, multiply the numbers under the square root.
$$\frac{12\sqrt{10}\sqrt{6}}{\sqrt{8}\sqrt{30}}$$
To multiply $\sqrt{10}$ and $\sqrt{6}$, multiply the numbers under the square root.
$$\frac{12\sqrt{60}}{\sqrt{8}\sqrt{30}}$$
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 $2^{2}$.
$$\frac{12\sqrt{60}}{2\sqrt{2}\sqrt{30}}$$
Factor $30=2\times 15$. Rewrite the square root of the product $\sqrt{2\times 15}$ as the product of square roots $\sqrt{2}\sqrt{15}$.
Factor $60=2^{2}\times 15$. Rewrite the square root of the product $\sqrt{2^{2}\times 15}$ as the product of square roots $\sqrt{2^{2}}\sqrt{15}$. Take the square root of $2^{2}$.
