Divide $\frac{\sqrt{32}+\sqrt{98}-\sqrt{50}}{\sqrt{72}}$ by $\frac{1}{\sqrt{2}}$ by multiplying $\frac{\sqrt{32}+\sqrt{98}-\sqrt{50}}{\sqrt{72}}$ by the reciprocal of $\frac{1}{\sqrt{2}}$.
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 $4^{2}$.
Factor $98=7^{2}\times 2$. Rewrite the square root of the product $\sqrt{7^{2}\times 2}$ as the product of square roots $\sqrt{7^{2}}\sqrt{2}$. Take the square root of $7^{2}$.
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 $5^{2}$.
Combine $11\sqrt{2}$ and $-5\sqrt{2}$ to get $6\sqrt{2}$.
$$\frac{6\sqrt{2}\sqrt{2}}{\sqrt{72}}$$
Multiply $\sqrt{2}$ and $\sqrt{2}$ to get $2$.
$$\frac{6\times 2}{\sqrt{72}}$$
Multiply $6$ and $2$ to get $12$.
$$\frac{12}{\sqrt{72}}$$
Factor $72=6^{2}\times 2$. Rewrite the square root of the product $\sqrt{6^{2}\times 2}$ as the product of square roots $\sqrt{6^{2}}\sqrt{2}$. Take the square root of $6^{2}$.
$$\frac{12}{6\sqrt{2}}$$
Rationalize the denominator of $\frac{12}{6\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
$$\frac{12\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$
The square of $\sqrt{2}$ is $2$.
$$\frac{12\sqrt{2}}{6\times 2}$$
Cancel out $2\times 6$ in both numerator and denominator.
