Factor $90=3^{2}\times 10$. Rewrite the square root of the product $\sqrt{3^{2}\times 10}$ as the product of square roots $\sqrt{3^{2}}\sqrt{10}$. Take the square root of $3^{2}$.
Factor $160=4^{2}\times 10$. Rewrite the square root of the product $\sqrt{4^{2}\times 10}$ as the product of square roots $\sqrt{4^{2}}\sqrt{10}$. Take the square root of $4^{2}$.
Combine $12\sqrt{10}$ and $-24\sqrt{10}$ to get $-12\sqrt{10}$.
$$-12\sqrt{10}+\sqrt{245}-5\sqrt{125}$$
Factor $245=7^{2}\times 5$. Rewrite the square root of the product $\sqrt{7^{2}\times 5}$ as the product of square roots $\sqrt{7^{2}}\sqrt{5}$. Take the square root of $7^{2}$.
$$-12\sqrt{10}+7\sqrt{5}-5\sqrt{125}$$
Factor $125=5^{2}\times 5$. Rewrite the square root of the product $\sqrt{5^{2}\times 5}$ as the product of square roots $\sqrt{5^{2}}\sqrt{5}$. Take the square root of $5^{2}$.
$$-12\sqrt{10}+7\sqrt{5}-5\times 5\sqrt{5}$$
Multiply $-5$ and $5$ to get $-25$.
$$-12\sqrt{10}+7\sqrt{5}-25\sqrt{5}$$
Combine $7\sqrt{5}$ and $-25\sqrt{5}$ to get $-18\sqrt{5}$.
