To find the product of \( 5 - \sqrt{16} \) and \( 16 \), we first calculate \( \sqrt{16} \).
\[ \sqrt{16} = 4 \]
Now, substituting this back into the expression, we have:
\[ 5 - \sqrt{16} = 5 - 4 = 1 \]
Next, we find the product of \( 1 \) and \( 16 \):
\[ 1 \times 16 = 16 \]
Now we determine the type of number this result is:
\( 16 \) is a rational number because it can be expressed as the ratio of two integers (for example, \( \frac{16}{1} \)).
So the answer is:
16; a rational number. However, this choice is not listed in your responses. If we apply similar reasoning, the correct option would refer to the predefined responses, which seem to focus on a calculation leading to a decimal approximation.
To clarify slightly, it appears there might be a confusion in the responses and the actual calculation leads to \( 16 \), indicating a rational number. However, if observing the options strictly, none directly reflect \( 16 \).
If any issues arise, please explore our calculations with a clear focus on \( 5 - \sqrt{16} \) leading to \( 16 \), concluding that it’s a rational number.