Which of the following defines irrational numbers?

Irrational numbers are defined as numbers that cannot be expressed as a simple fraction, meaning they cannot be written in the form of ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b ) is not zero.

The correct choice mentions examples like 3.14 and negative square roots. It's important to clarify that while 3.14 is actually a rounded representation of the irrational number ( \pi ), which itself cannot be expressed as a fraction, the reference to negative square roots can be a bit misleading since negative square roots are not irrational in the traditional sense. For instance, the square root of -1 is imaginary, not irrational.

The essential point is that irrational numbers include values like ( \pi ) and the square root of non-perfect squares (like the square root of 2), which cannot be accurately expressed as fractions, unlike rational numbers, which can. Therefore, this definition encompasses both well-known constants and certain roots that are not perfect squares, helping to clarify their unique position in the number system.

In contrast, fractions are categorized under rational numbers, whole numbers are a subset of integers, and perfect squares represent a specific group of numbers (