Ms. Arrowood is classifying the number √-18 . Is Ms. Arrowood correct or incorrect? How do you know?

To classify the number \( \sqrt{-18} \), we need to consider the properties of square roots and the nature of numbers.

1. The square root of a negative number is not a real number. Instead, it is classified as an imaginary number. In this case, we can simplify \( \sqrt{-18} \):
\[
\sqrt{-18} = \sqrt{-1 \cdot 18} = \sqrt{-1} \cdot \sqrt{18} = i\sqrt{18}
\]
where \( i \) is the imaginary unit, defined as \( i = \sqrt{-1} \).

2. We can further simplify \( \sqrt{18} \):
\[
\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
\]
Thus,
\[
\sqrt{-18} = i \cdot 3\sqrt{2} = 3\sqrt{2}i.
\]

From this analysis, we can conclude that \( \sqrt{-18} \) is indeed an imaginary number. Therefore, if Ms. Arrowood stated that \( \sqrt{-18} \) is an imaginary number, she is correct. If she classified it as a real number, she would be incorrect.