Find the Complex Conjugate square root of -20

$\sqrt{- 20}$

Rewrite $- 20$ as $- 1 (20)$ .

$\sqrt{- 1 (20)}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$\sqrt{- 1} \cdot \sqrt{20}$

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

$i \cdot \sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

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Factor $4$ out of $20$ .

$i \cdot \sqrt{4 (5)}$

Rewrite $4$ as $2^{2}$ .

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

Pull terms out from under the radical.

$i \cdot (2 \sqrt{5})$

Move $2$ to the left of $i$ .

$2 i \sqrt{5}$

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

$- 2 i \sqrt{5}$