If $9x^2 + 24x + a$ is the square of a binomial, then it must be of the form $(3x + b)^2$ for some constant $b$.
Expanding, we have $(3x + b)^2 = 9x^2 + 6bx + b^2$.
Comparing the coefficients, we see that $6b = 24$, so $b = 4$, and $b^2 = 16$.
Therefore, $a = \boxed{16}$.
The answer is: 16
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If $a$ is a constant such that $9x^2 + 24x + a$ is the square of a binomial, then what is $a$?

### Answer:
