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 $2^{2}$.
$$2\times 2\sqrt{2}-3\sqrt{98}-2\sqrt{200}$$
Multiply $2$ and $2$ to get $4$.
$$4\sqrt{2}-3\sqrt{98}-2\sqrt{200}$$
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 $7^{2}$.
$$4\sqrt{2}-3\times 7\sqrt{2}-2\sqrt{200}$$
Multiply $-3$ and $7$ to get $-21$.
$$4\sqrt{2}-21\sqrt{2}-2\sqrt{200}$$
Combine $4\sqrt{2}$ and $-21\sqrt{2}$ to get $-17\sqrt{2}$.
$$-17\sqrt{2}-2\sqrt{200}$$
Factor $200=10^{2}\times 2$. Rewrite the square root of the product $\sqrt{10^{2}\times 2}$ as the product of square roots $\sqrt{10^{2}}\sqrt{2}$. Take the square root of $10^{2}$.
$$-17\sqrt{2}-2\times 10\sqrt{2}$$
Multiply $-2$ and $10$ to get $-20$.
$$-17\sqrt{2}-20\sqrt{2}$$
Combine $-17\sqrt{2}$ and $-20\sqrt{2}$ to get $-37\sqrt{2}$.
