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

Answer 1

To classify the number \( -\sqrt{18} \) (which can also be expressed as \( -\sqrt{9 \times 2} = -3\sqrt{2} \)), we need to determine its properties.

1. Real vs. Imaginary: The square root of a positive number, like 18, is a real number. Since Ms. Arrowood has the negative of a real number, \( -\sqrt{18} \) is also a real number.

2. Rational vs. Irrational: The square root of 18 simplifies to \( 3\sqrt{2} \). Since \( \sqrt{2} \) is known to be an irrational number, \( 3\sqrt{2} \) is also irrational. Therefore, \( -\sqrt{18} \) is still an irrational number because the negative of an irrational number remains irrational.

Conclusion: Ms. Arrowood is correct in identifying \( -\sqrt{18} \) as a real number and an irrational number.