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 $3^{2}$.
$$8+\frac{\sqrt{3\times 3\sqrt{2}}}{8+9}$$
Multiply $3$ and $3$ to get $9$.
$$8+\frac{\sqrt{9\sqrt{2}}}{8+9}$$
Add $8$ and $9$ to get $17$.
$$8+\frac{\sqrt{9\sqrt{2}}}{17}$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $8$ times $\frac{17}{17}$.
