To simplify the expression \( \sqrt{\frac{16}{144}} \), we can first simplify the fraction inside the square root:
\[ \frac{16}{144} = \frac{1}{9} \]
Now, we take the square root of \( \frac{1}{9} \):
\[ \sqrt{\frac{1}{9}} = \frac{\sqrt{1}}{\sqrt{9}} = \frac{1}{3} \]
Thus, the simplified form of the expression \( \sqrt{\frac{16}{144}} \) is:
\[ \frac{1}{3} \]