To find the quotient of \(\frac{\sqrt{49}}{\sqrt{121}}\), we first need to simplify both square roots:
\[ \sqrt{49} = 7 \] \[ \sqrt{121} = 11 \]
Now, we can rewrite the fraction:
\[ \frac{\sqrt{49}}{\sqrt{121}} = \frac{7}{11} \]
Since the fraction \(\frac{7}{11}\) is already in simplest form and the denominator is rational, we do not need to rationalize it further.
Thus, the final answer is:
\[ \frac{7}{11} \]