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

Question

she say it is real number. there is no i

Answer 1

To determine whether Ms. Arrowood's classification of the number \(-\sqrt{18}\) as a real number is correct, we need to analyze the expression.

The expression \(-\sqrt{18}\) can be further simplified:

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

So, \(-\sqrt{18} = -3\sqrt{2}\).

Since \(\sqrt{2}\) is a real number, \(-3\sqrt{2}\) is also a real number because any real number multiplied by another real number results in a real number.

Thus, \(-\sqrt{18}\) is indeed a real number.

Conclusion: Ms. Arrowood is correct in classifying \(-\sqrt{18}\) as a real number, as it is a valid operation that results in a real number without involving imaginary numbers (\(i\)).