The problem asks us to simplify the square root of a fraction: $\sqrt{\frac{64}{9}}$.

1. Problem Description

The problem asks us to simplify the square root of a fraction: $\sqrt{\frac{64}{9}}$.

2. Solution Steps

We can simplify the square root of a fraction by taking the square root of the numerator and the square root of the denominator separately.

$$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$

In this case, we have:

$$\sqrt{\frac{64}{9}} = \frac{\sqrt{64}}{\sqrt{9}}$$

We know that $\sqrt{64} = 8$ and $\sqrt{9} = 3$. Therefore,

$$\frac{\sqrt{64}}{\sqrt{9}} = \frac{8}{3}$$

3. Final Answer

$\frac{8}{3}$