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 $5^{2}$.
$$D=5\sqrt{2}+2\sqrt{20}+\sqrt{80}-\sqrt{500}$$
Factor $20=2^{2}\times 5$. Rewrite the square root of the product $\sqrt{2^{2}\times 5}$ as the product of square roots $\sqrt{2^{2}}\sqrt{5}$. Take the square root of $2^{2}$.
Factor $80=4^{2}\times 5$. Rewrite the square root of the product $\sqrt{4^{2}\times 5}$ as the product of square roots $\sqrt{4^{2}}\sqrt{5}$. Take the square root of $4^{2}$.
$$D=5\sqrt{2}+4\sqrt{5}+4\sqrt{5}-\sqrt{500}$$
Combine $4\sqrt{5}$ and $4\sqrt{5}$ to get $8\sqrt{5}$.
$$D=5\sqrt{2}+8\sqrt{5}-\sqrt{500}$$
Factor $500=10^{2}\times 5$. Rewrite the square root of the product $\sqrt{10^{2}\times 5}$ as the product of square roots $\sqrt{10^{2}}\sqrt{5}$. Take the square root of $10^{2}$.
$$D=5\sqrt{2}+8\sqrt{5}-10\sqrt{5}$$
Combine $8\sqrt{5}$ and $-10\sqrt{5}$ to get $-2\sqrt{5}$.
