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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:
\[
\sqrt{35}
\]