Simplify square root of 3* square root of -4

$\sqrt{3} \cdot \sqrt{- 4}$

Rewrite $- 4$ as $- 1 (4)$ .

$\sqrt{3} \cdot \sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\sqrt{3} \cdot (\sqrt{- 1} \cdot \sqrt{4})$

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

$\sqrt{3} \cdot (i \cdot \sqrt{4})$

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

$\sqrt{3} \cdot (i \cdot \sqrt{2^{2}})$

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

$\sqrt{3} \cdot (i \cdot 2)$

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

$\sqrt{3} \cdot (2 \cdot i)$

Move $2$ to the left of $\sqrt{3}$ .

$2 \sqrt{3} i$