We have $\sqrt{3^3 + 3^3 + 3^3} = \sqrt{27 + 27 + 27}$.
Simplifying, we get $\sqrt{81}$.
Since $\sqrt{81} = 9$, the value is $\boxed{9}$.
The answer is: 9
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the value of $\sqrt{3^3 + 3^3 + 3^3}$?

### Answer:
