Find the Complex Conjugate square root of -25

$\sqrt{- 25}$

Rewrite $- 25$ as $- 1 (25)$ .

$\sqrt{- 1 (25)}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$\sqrt{- 1} \cdot \sqrt{25}$

Rewrite $\sqrt{- 1}$ as $i$ .

$i \cdot \sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$i \cdot \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 5$

Move $5$ to the left of $i$ .

$5 i$

To find the complex conjugate, negate the term with $i$ .

$- 5 i$