Question

Ms. Arrowood is classifying the number −18−−−−√ . ms. arrowood says this number is real , there is no i . Is Ms. Arrowood correct or incorrect? How do you know?

Answer 1

Ms. Arrowood is incorrect in classifying the number \(-\sqrt{18}\) as a real number.

The number \(-\sqrt{18}\) simplifies to \(-3\sqrt{2}\), which is indeed a real number. However, if she is referring to the square root of a negative number (for example, if she had intended to write \(-\sqrt{-18}\)), then it would involve the imaginary unit \(i\). The expression \(-\sqrt{-18}\) can be rewritten as \(-\sqrt{18}i\), which is complex and includes the imaginary unit \(i\).

To summarize:
- If the expression is \(-\sqrt{18}\), it is a real number.
- If the expression is \(-\sqrt{-18}\), it includes an imaginary component and is not a real number.

Without clarification of the expression, it seems likely Ms. Arrowood was discussing \(-\sqrt{18}\), which is correct to classify as real. However, if she was considering a negative under the square root, she would be incorrect in saying there is no \(i\).