Factor $242=11^{2}\times 2$. Rewrite the square root of the product $\sqrt{11^{2}\times 2}$ as the product of square roots $\sqrt{11^{2}}\sqrt{2}$. Take the square root of $11^{2}$.
$$7\times 11\sqrt{2}+11\sqrt{242}+13\sqrt{242}$$
Multiply $7$ and $11$ to get $77$.
$$77\sqrt{2}+11\sqrt{242}+13\sqrt{242}$$
Factor $242=11^{2}\times 2$. Rewrite the square root of the product $\sqrt{11^{2}\times 2}$ as the product of square roots $\sqrt{11^{2}}\sqrt{2}$. Take the square root of $11^{2}$.
$$77\sqrt{2}+11\times 11\sqrt{2}+13\sqrt{242}$$
Multiply $11$ and $11$ to get $121$.
$$77\sqrt{2}+121\sqrt{2}+13\sqrt{242}$$
Combine $77\sqrt{2}$ and $121\sqrt{2}$ to get $198\sqrt{2}$.
$$198\sqrt{2}+13\sqrt{242}$$
Factor $242=11^{2}\times 2$. Rewrite the square root of the product $\sqrt{11^{2}\times 2}$ as the product of square roots $\sqrt{11^{2}}\sqrt{2}$. Take the square root of $11^{2}$.
$$198\sqrt{2}+13\times 11\sqrt{2}$$
Multiply $13$ and $11$ to get $143$.
$$198\sqrt{2}+143\sqrt{2}$$
Combine $198\sqrt{2}$ and $143\sqrt{2}$ to get $341\sqrt{2}$.
