The number \( 2\sqrt{3} \) is an irrational number.
Here's a brief explanation of the other numbers:
- \( -1529 \) is a rational number (it's an integer).
- \( 0.343434...\) (which can be written as \( 0.\overline{34} \)) is a rational number because it can be expressed as a fraction.
- \( 87.9821 \) is also a rational number since it can be expressed as a fraction (it's a terminating decimal).
Thus, the only irrational number in the list is \( 2\sqrt{3} \).