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 $5^{2}$.
$$4\times 5\sqrt{2}+\sqrt{200}-\sqrt{50}$$
Multiply $4$ and $5$ to get $20$.
$$20\sqrt{2}+\sqrt{200}-\sqrt{50}$$
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 $10^{2}$.
$$20\sqrt{2}+10\sqrt{2}-\sqrt{50}$$
Combine $20\sqrt{2}$ and $10\sqrt{2}$ to get $30\sqrt{2}$.
$$30\sqrt{2}-\sqrt{50}$$
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 $5^{2}$.
$$30\sqrt{2}-5\sqrt{2}$$
Combine $30\sqrt{2}$ and $-5\sqrt{2}$ to get $25\sqrt{2}$.
