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 $7^{2}$.
$$7\sqrt{2}+5\sqrt{72}+9\sqrt{8}$$
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 $6^{2}$.
$$7\sqrt{2}+5\times 6\sqrt{2}+9\sqrt{8}$$
Multiply $5$ and $6$ to get $30$.
$$7\sqrt{2}+30\sqrt{2}+9\sqrt{8}$$
Combine $7\sqrt{2}$ and $30\sqrt{2}$ to get $37\sqrt{2}$.
$$37\sqrt{2}+9\sqrt{8}$$
Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$37\sqrt{2}+9\times 2\sqrt{2}$$
Multiply $9$ and $2$ to get $18$.
$$37\sqrt{2}+18\sqrt{2}$$
Combine $37\sqrt{2}$ and $18\sqrt{2}$ to get $55\sqrt{2}$.
