To multiply \( \sqrt{11} \) by \( \sqrt{67} \), you can use the property of square roots that states:
\[ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \]
Applying this property:
\[ \sqrt{11} \cdot \sqrt{67} = \sqrt{11 \cdot 67} \]
Now, calculate \( 11 \cdot 67 \):
\[ 11 \cdot 67 = 737 \]
Thus,
\[ \sqrt{11} \cdot \sqrt{67} = \sqrt{737} \]
So, the exact answer is:
\[ \sqrt{737} \]