Factor $384=8^{2}\times 6$. Rewrite the square root of the product $\sqrt{8^{2}\times 6}$ as the product of square roots $\sqrt{8^{2}}\sqrt{6}$. Take the square root of $8^{2}$.
$$\frac{24\times 8\sqrt{6}}{8}\sqrt{98}$$
Multiply $24$ and $8$ to get $192$.
$$\frac{192\sqrt{6}}{8}\sqrt{98}$$
Divide $192\sqrt{6}$ by $8$ to get $24\sqrt{6}$.
$$24\sqrt{6}\sqrt{98}$$
Factor $98=7^{2}\times 2$. Rewrite the square root of the product $\sqrt{7^{2}\times 2}$ as the product of square roots $\sqrt{7^{2}}\sqrt{2}$. Take the square root of $7^{2}$.
$$24\sqrt{6}\times 7\sqrt{2}$$
Multiply $24$ and $7$ to get $168$.
$$168\sqrt{6}\sqrt{2}$$
Factor $6=2\times 3$. Rewrite the square root of the product $\sqrt{2\times 3}$ as the product of square roots $\sqrt{2}\sqrt{3}$.
