Evaluate square root of -4- square root of -9

$\sqrt{- 4} - \sqrt{- 9}$

Step 1

Simplify each term.

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

$\sqrt{- 1 (4)} - \sqrt{- 9}$

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

$\sqrt{- 1} \cdot \sqrt{4} - \sqrt{- 9}$

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

$i \cdot \sqrt{4} - \sqrt{- 9}$

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

$i \cdot \sqrt{2^{2}} - \sqrt{- 9}$

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

$i \cdot 2 - \sqrt{- 9}$

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

$2 \cdot i - \sqrt{- 9}$

Rewrite $- 9$ as $- 1 (9)$ .

$2 i - \sqrt{- 1 (9)}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$2 i - (\sqrt{- 1} \cdot \sqrt{9})$

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

$2 i - (i \cdot \sqrt{9})$

Rewrite $9$ as $3^{2}$ .

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

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

$2 i - (i \cdot 3)$

Move $3$ to the left of $i$ .

$2 i - (3 \cdot i)$

Multiply $3$ by $- 1$ .

$2 i - 3 i$

Step 2

Subtract $3 i$ from $2 i$ .

$- i$