Question

Ms. Arrowood is classifying the number √-18 . Is Ms. Arrowood correct or incorrect? How do you know?
she say it is a real number,there no i

Answer 1

Ms. Arrowood is incorrect in classifying the number \(\sqrt{-18}\) as a real number. The square root of a negative number is not a real number; instead, it is an imaginary number.

To express \(\sqrt{-18}\), we can break it down:

\[
\sqrt{-18} = \sqrt{18} \cdot \sqrt{-1}
\]

Since \(\sqrt{-1}\) is defined as the imaginary unit \(i\), we have:

\[
\sqrt{-18} = \sqrt{18} \cdot i
\]

We can simplify \(\sqrt{18}\):

\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
\]

Therefore,

\[
\sqrt{-18} = 3\sqrt{2} \cdot i
\]

In summary, \(\sqrt{-18}\) is an imaginary number (specifically \(3\sqrt{2}i\)), and therefore it is not a real number.