multiply \sqrt{2}\left(11-\sqrt{7}\right)
To multiply \(\sqrt{2}\left(11-\sqrt{7}\right)\), you need to distribute the square root of 2 to both terms inside the parentheses:
\[\sqrt{2}\left(11-\sqrt{7}\right) = 11\sqrt{2}-\sqrt{2}\sqrt{7}.\]
Since \(\sqrt{2}\sqrt{7} = \sqrt{14}\), the expression simplifies to:
\[11\sqrt{2}-\sqrt{14}.\]
Therefore, \(\sqrt{2}\left(11-\sqrt{7}\right) = 11\sqrt{2}-\sqrt{14}\).