To analyze the expression \( 19 - \sqrt{-32} \), we first note that \( \sqrt{-32} \) involves taking the square root of a negative number, which results in an imaginary number:
\[ \sqrt{-32} = \sqrt{32} \cdot \sqrt{-1} = \sqrt{32}i \]
Since \( \sqrt{32} = 4\sqrt{2} \), we can rewrite it as:
\[ \sqrt{-32} = 4\sqrt{2}i \]
Now substituting this back into the original expression, we have:
\[ 19 - \sqrt{-32} = 19 - 4\sqrt{2}i \]
This results in a complex number, which includes a real part (19) and an imaginary part \(-4\sqrt{2}i\).
In terms of the answer options given:
- An irrational number: This refers to numbers that cannot be expressed as a fraction (not applicable here since we have a complex number).
- A whole number: Whole numbers are non-negative integers, which does not apply as we have an imaginary component.
- An integer: Integers are whole numbers that can be positive, negative, or zero. However, this expression includes an imaginary component, so it is not an integer.
- A rational number: Rational numbers are numbers that can be expressed as a fraction of integers. But again, due to the imaginary component, it cannot be considered rational.
Since the expression results in a complex number, which is not included in the options, this specific number type is typically categorized as a complex number.
However, if forced to choose one of the given responses based on the information we evaluated, none of the responses truly fit the nature of the result (as it's complex). If necessary to answer based on available choices, note that the expression clearly does not fall into irrational, whole, integer, or rational classifications, thus none of the options are accurate descriptions for \( 19 - \sqrt{-32} \).