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 $5^{2}$.
$$5\sqrt{2}-8\sqrt{9}+\sqrt{162}$$
Calculate the square root of $9$ and get $3$.
$$5\sqrt{2}-8\times 3+\sqrt{162}$$
Multiply $-8$ and $3$ to get $-24$.
$$5\sqrt{2}-24+\sqrt{162}$$
Factor $162=9^{2}\times 2$. Rewrite the square root of the product $\sqrt{9^{2}\times 2}$ as the product of square roots $\sqrt{9^{2}}\sqrt{2}$. Take the square root of $9^{2}$.
$$5\sqrt{2}-24+9\sqrt{2}$$
Combine $5\sqrt{2}$ and $9\sqrt{2}$ to get $14\sqrt{2}$.
