To determine which option best describes the number [tex]\( \sqrt{-7} \)[/tex], we need to analyze the nature of the square root of a negative number.
1. Understanding the square root of a negative number:
- The square root of a negative number involves the concept of imaginary numbers.
- For any negative number under the square root, the result is not a real number but an imaginary one.
2. Breaking down [tex]\(\sqrt{-7}\)[/tex]:
- The expression [tex]\(\sqrt{-7}\)[/tex] can be rewritten using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].
- Therefore, [tex]\(\sqrt{-7} = \sqrt{7} \cdot \sqrt{-1} = \sqrt{7} \cdot i \)[/tex].
3. Classifying [tex]\(\sqrt{-7}\)[/tex]:
- Since [tex]\(\sqrt{-7}\)[/tex] involves the imaginary unit [tex]\(i\)[/tex], it is classified as an imaginary number.
4. Evaluating the given options:
- Option A: Composite - A composite number is a positive integer that has at least one positive divisor other than 1 and itself. This does not apply to [tex]\(\sqrt{-7}\)[/tex].
- Option B: Positive - The concept of positivity applies to real numbers. Imaginary numbers do not fall under the classification of positive or negative.
- Option C: Perfect square - A perfect square is an integer that is the square of another integer. [tex]\(\sqrt{-7}\)[/tex] is not an integer, and 7 is not a perfect square when considering real numbers.
- Option D: Imaginary - This option correctly describes [tex]\(\sqrt{-7}\)[/tex] as it is a number that includes the imaginary unit [tex]\(i\)[/tex].
Based on the analysis, the correct description of [tex]\(\sqrt{-7}\)[/tex] is:
[tex]\[ \boxed{\text{Imaginary}} \][/tex]
Therefore, the best description for the number [tex]\(\sqrt{-7}\)[/tex] is D. Imaginary.
