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 $i$ .

$11 i$