To simplify [tex]\(-\sqrt{-75}\)[/tex]:
1. Recognize that the expression involves the square root of a negative number. We can address this by factoring out [tex]\(-1\)[/tex] from under the square root:
[tex]\[ -\sqrt{-75} = -\sqrt{-1 \cdot 75} \][/tex]
2. The square root of [tex]\(-1\)[/tex] is denoted as [tex]\(i\)[/tex], the imaginary unit:
[tex]\[ -\sqrt{-1 \cdot 75} = -\sqrt{-1} \cdot \sqrt{75} = -i \cdot \sqrt{75} \][/tex]
3. Simplify [tex]\(\sqrt{75}\)[/tex]:
[tex]\[ 75 = 25 \cdot 3 \][/tex]
[tex]\[ \sqrt{75} = \sqrt{25 \cdot 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3} \][/tex]
4. Substituting back:
[tex]\[ -i \cdot \sqrt{75} = -i \cdot 5\sqrt{3} = -5i\sqrt{3} \][/tex]
Therefore, the simplified expression for [tex]\(-\sqrt{-75}\)[/tex] is:
[tex]\[ -5i\sqrt{3} \][/tex]
So, the correct answer is:
A. [tex]\(-5 i \sqrt{3}\)[/tex]
