Simplify 2i^2 square root of -75

$2 i^{2} \sqrt{- 75}$

Step 1

Rewrite $- 75$ as $- 1 (75)$ .

$2 i^{2} \sqrt{- 1 (75)}$

Step 2

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$2 i^{2} (\sqrt{- 1} \cdot \sqrt{75})$

Step 3

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

$2 i^{2} (i \cdot \sqrt{75})$

Step 4

Rewrite $i^{2}$ as $- 1$ .

$2 \cdot - 1 (i \cdot \sqrt{75})$

Step 5

Multiply $2$ by $- 1$ .

$- 2 (i \cdot \sqrt{75})$

Step 6

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$- 2 (i \cdot \sqrt{25 (3)})$

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

$- 2 (i \cdot \sqrt{5^{2} \cdot 3})$

Step 7

Pull terms out from under the radical.

$- 2 (i \cdot (5 \sqrt{3}))$

Step 8

Simplify the expression.

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

$- 2 (5 \cdot i \sqrt{3})$

Multiply $5$ by $- 2$ .

$- 10 i \sqrt{3}$