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 $5^{2}$.
$$5\sqrt{2}-2\sqrt{8}-13\sqrt{18}-7\sqrt{2}$$
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 $2^{2}$.
Combine $5\sqrt{2}$ and $-4\sqrt{2}$ to get $\sqrt{2}$.
$$\sqrt{2}-13\sqrt{18}-7\sqrt{2}$$
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 $3^{2}$.
$$\sqrt{2}-13\times 3\sqrt{2}-7\sqrt{2}$$
Multiply $-13$ and $3$ to get $-39$.
$$\sqrt{2}-39\sqrt{2}-7\sqrt{2}$$
Combine $\sqrt{2}$ and $-39\sqrt{2}$ to get $-38\sqrt{2}$.
$$-38\sqrt{2}-7\sqrt{2}$$
Combine $-38\sqrt{2}$ and $-7\sqrt{2}$ to get $-45\sqrt{2}$.
