To determine which word best describes the number [tex]\( -\sqrt{3} \)[/tex], let's analyze it in detail:
1. Understand the nature of [tex]\( -\sqrt{3} \)[/tex]:
- [tex]\( \sqrt{3} \)[/tex] represents the square root of 3. Since 3 is not a perfect square, [tex]\( \sqrt{3} \)[/tex] is an irrational number.
- [tex]\( -\sqrt{3} \)[/tex] is simply the negative of [tex]\( \sqrt{3} \)[/tex], which means it is also irrational as the property of being irrational is preserved under negation.
2. Check the options:
- A. Rational: A rational number is any number that can be written as the quotient of two integers (i.e., [tex]\(\frac{a}{b}\)[/tex] where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers and [tex]\(b \neq 0\)[/tex]). Since [tex]\( -\sqrt{3} \)[/tex] cannot be written as such a quotient, it is not a rational number.
- B. Inrational: This seems to be a typographical error and likely meant to be "irrational." An irrational number cannot be expressed as the quotient of two integers, which matches the nature of [tex]\( -\sqrt{3} \)[/tex].
- C. Undefined: A number that is undefined does not have a value in the real number system. Examples include division by zero or certain limits. However, [tex]\( -\sqrt{3} \)[/tex] is well-defined as a real number.
- D. Non-real: Non-real numbers include imaginary and complex numbers. [tex]\( -\sqrt{3} \)[/tex] is not an imaginary or complex number; it is a real number.
Based on this analysis, the best word to describe [tex]\( -\sqrt{3} \)[/tex] is "irrational."
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
