In order to prove that the sum of two rational numbers is rational, the value you should use for \( a \) is 3.
The rationale is that 3 is a rational number (it can be expressed as a ratio of integers, namely \( \frac{3}{1} \)). The other options provided (π, \( \sqrt{3} \), and 30) are not appropriate for proving the statement regarding rational numbers:
- π is an irrational number.
- \( \sqrt{3} \) is also an irrational number.
- 30 is a rational number, but it doesn't necessarily relate to the expression \( a + cbd \) in the same way as 3 does.
Thus, using 3 as the value for \( a \) would help you establish the rational nature of the sum.