To classify the number \( \sqrt{-18} \), we need to consider the properties of square roots and the nature of numbers.
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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 \( i = \sqrt{-1} \).
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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.
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