Factor $176=4^{2}\times 11$. Rewrite the square root of the product $\sqrt{4^{2}\times 11}$ as the product of square roots $\sqrt{4^{2}}\sqrt{11}$. Take the square root of $4^{2}$.
Factor $45=3^{2}\times 5$. Rewrite the square root of the product $\sqrt{3^{2}\times 5}$ as the product of square roots $\sqrt{3^{2}}\sqrt{5}$. Take the square root of $3^{2}$.
Factor $320=8^{2}\times 5$. Rewrite the square root of the product $\sqrt{8^{2}\times 5}$ as the product of square roots $\sqrt{8^{2}}\sqrt{5}$. Take the square root of $8^{2}$.
Combine $-2\sqrt{5}$ and $\sqrt{5}$ to get $-\sqrt{5}$.
$$3\sqrt{11}-\sqrt{5}+\frac{1}{5}\sqrt{275}$$
Factor $275=5^{2}\times 11$. Rewrite the square root of the product $\sqrt{5^{2}\times 11}$ as the product of square roots $\sqrt{5^{2}}\sqrt{11}$. Take the square root of $5^{2}$.
