Factor $220=2^{2}\times 55$. Rewrite the square root of the product $\sqrt{2^{2}\times 55}$ as the product of square roots $\sqrt{2^{2}}\sqrt{55}$. Take the square root of $2^{2}$.
$$\frac{12\times 2\sqrt{55}}{3}\sqrt{120}$$
Multiply $12$ and $2$ to get $24$.
$$\frac{24\sqrt{55}}{3}\sqrt{120}$$
Divide $24\sqrt{55}$ by $3$ to get $8\sqrt{55}$.
$$8\sqrt{55}\sqrt{120}$$
Factor $120=2^{2}\times 30$. Rewrite the square root of the product $\sqrt{2^{2}\times 30}$ as the product of square roots $\sqrt{2^{2}}\sqrt{30}$. Take the square root of $2^{2}$.
$$8\sqrt{55}\times 2\sqrt{30}$$
Multiply $8$ and $2$ to get $16$.
$$16\sqrt{55}\sqrt{30}$$
To multiply $\sqrt{55}$ and $\sqrt{30}$, multiply the numbers under the square root.
$$16\sqrt{1650}$$
Factor $1650=5^{2}\times 66$. Rewrite the square root of the product $\sqrt{5^{2}\times 66}$ as the product of square roots $\sqrt{5^{2}}\sqrt{66}$. Take the square root of $5^{2}$.
