Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.
Combine $3\sqrt{2}$ and $-20\sqrt{2}$ to get $-17\sqrt{2}$.
$$-17\sqrt{2}+7\sqrt{8}-9\sqrt{50}$$
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 $2^{2}$.
$$-17\sqrt{2}+7\times 2\sqrt{2}-9\sqrt{50}$$
Multiply $7$ and $2$ to get $14$.
$$-17\sqrt{2}+14\sqrt{2}-9\sqrt{50}$$
Combine $-17\sqrt{2}$ and $14\sqrt{2}$ to get $-3\sqrt{2}$.
$$-3\sqrt{2}-9\sqrt{50}$$
Factor $50=5^{2}\times 2$. Rewrite the square root of the product $\sqrt{5^{2}\times 2}$ as the product of square roots $\sqrt{5^{2}}\sqrt{2}$. Take the square root of $5^{2}$.
$$-3\sqrt{2}-9\times 5\sqrt{2}$$
Multiply $-9$ and $5$ to get $-45$.
$$-3\sqrt{2}-45\sqrt{2}$$
Combine $-3\sqrt{2}$ and $-45\sqrt{2}$ to get $-48\sqrt{2}$.
