Answer
$\frac{8}{11}$
Work Step by Step
According to the quotient product of radicals, $\sqrt[n] \frac{a}{b}=\frac{\sqrt[n] a}{\sqrt[n] b}$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots.
Therefore, $\sqrt \frac{64}{121}=\frac{\sqrt 64}{\sqrt 121}=\frac{8}{11}$.
$\sqrt 64=8$, because $8^{2}=64$
$\sqrt 121=11$, because $11^{2}=121$