To solve the problem [tex]\(18 - \sqrt{-25}\)[/tex], we need to understand how to handle the square root of a negative number.
1. Identify the square root of the negative number:
[tex]\[
\sqrt{-25}
\][/tex]
We know that the square root of a negative number involves imaginary numbers. Specifically,
[tex]\[
\sqrt{-25} = \sqrt{25 \cdot (-1)} = \sqrt{25} \cdot \sqrt{-1} = 5i
\][/tex]
Here, [tex]\(i\)[/tex] represents the imaginary unit, where [tex]\(i = \sqrt{-1}\)[/tex].
2. Substitute this back into the original expression:
[tex]\[
18 - \sqrt{-25} = 18 - 5i
\][/tex]
Therefore, the expression [tex]\(18 - \sqrt{-25}\)[/tex] simplifies to [tex]\(18 - 5i\)[/tex].
The correct answer is:
[tex]\[
\boxed{18-5i}
\][/tex]
