Final answer:
The irrational number among the options listed is A) √6, because it is a non-terminating and non-repeating decimal that cannot be expressed as a ratio of two integers.
Step-by-step explanation:
Among the provided options, the number \(√6\) is irrational. This is because the square root of 6 cannot be expressed as a ratio of two integers; the decimal form of \(√6\) is non-terminating and non-repeating. On the other hand, options B (4.3) and D (-5/9) are rational numbers, as they can be expressed as fractions or terminating decimals. Option C (1.618) seems like it could be the golden ratio, which is irrational, but as it's written here as a terminated decimal, it is considered a rational approximation. Thus, the only option that is guaranteed to be irrational is A) \(√6\).