To complete the expression and narrow the interval \( \sqrt{164} \), we first need to calculate it.
Calculating \( \sqrt{164} \):
- The closest perfect squares to 164 are \( 144 \) (which is \( 12^2 \)) and \( 169 \) (which is \( 13^2 \)).
- Therefore, we know that \( 12 < \sqrt{164} < 13 \).
Now, we can refine this by estimating \( \sqrt{164} \) more closely. Using a calculator, we find:
\[ \sqrt{164} \approx 12.806 \]
Rounding to the nearest tenth gives us:
\[ \sqrt{164} \approx 12.8 \]
Thus, we can complete the expression that narrows the interval:
\[ 12.8 < \sqrt{164} < 12.9 \]
So the final interval is:
\[ \boxed{(12.8, 12.9)} \]