Simplify - square root of -121

$- \sqrt{- 121}$

Step 1

Rewrite $- 121$ as $- 1 (121)$ .

$- \sqrt{- 1 (121)}$

Step 2

Rewrite $\sqrt{- 1 (121)}$ as $\sqrt{- 1} \cdot \sqrt{121}$ .

$- (\sqrt{- 1} \cdot \sqrt{121})$

Step 3

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

$- (i \cdot \sqrt{121})$

Step 4

Rewrite $121$ as $11^{2}$ .

$- (i \cdot \sqrt{11^{2}})$

Step 5

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

$- (i \cdot 11)$

Step 6

Move $11$ to the left of $i$ .

$- (11 \cdot i)$

Step 7

Multiply $11$ by $- 1$ .

$- 11 i$