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 $5^{2}$.
$$\frac{5\sqrt{2}+\sqrt{18}}{\sqrt{32}}$$
Factor $18=3^{2}\times 2$. Rewrite the square root of the product $\sqrt{3^{2}\times 2}$ as the product of square roots $\sqrt{3^{2}}\sqrt{2}$. Take the square root of $3^{2}$.
$$\frac{5\sqrt{2}+3\sqrt{2}}{\sqrt{32}}$$
Combine $5\sqrt{2}$ and $3\sqrt{2}$ to get $8\sqrt{2}$.
$$\frac{8\sqrt{2}}{\sqrt{32}}$$
Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.
$$\frac{8\sqrt{2}}{4\sqrt{2}}$$
Cancel out $4\sqrt{2}$ in both numerator and denominator.
