Multiply square root of 11-6 by square root of seven given an exact answer

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:

\[
\sqrt{35}
\]