Answer :

To solve for [tex]\(\sqrt{-5}\)[/tex] given that [tex]\(x \geq 0\)[/tex] and [tex]\(\sqrt{-x} = i \sqrt{x}\)[/tex]:

1. Identify the value of [tex]\(x\)[/tex]:
Here, we are given [tex]\(x = 5\)[/tex].

2. Substitute [tex]\(x\)[/tex] into the equation:
We need to find [tex]\(\sqrt{-5}\)[/tex].
According to the given condition, [tex]\(\sqrt{-x} = i \sqrt{x}\)[/tex].

3. Apply the formula:
Substitute [tex]\(x = 5\)[/tex] into the formula:
[tex]\[ \sqrt{-5} = i \sqrt{5} \][/tex]

4. Calculate [tex]\(\sqrt{5}\)[/tex]:

The value of [tex]\(\sqrt{5}\)[/tex] is approximately 2.23606797749979.

5. Multiply by [tex]\(i\)[/tex]:

Thus,
[tex]\[ \sqrt{-5} = i \cdot 2.23606797749979 \][/tex]

6. Result:
Hence, the value of [tex]\(\sqrt{-5}\)[/tex] is:
[tex]\[ 2.23606797749979j \][/tex]