To multiply \(\sqrt{11 - 6}\) by \(\sqrt{7}\), first simplify \(\sqrt{11 - 6}\):
\[ 11 - 6 = 5 \]
Thus, \(\sqrt{11 - 6} = \sqrt{5}\).
Now, multiply \(\sqrt{5}\) by \(\sqrt{7}\):
\[ \sqrt{5} \cdot \sqrt{7} = \sqrt{5 \cdot 7} = \sqrt{35} \]
Therefore, the exact answer is:
\[ \sqrt{35} \]