Evaluate square root of -25- square root of -4

$\sqrt{- 25} - \sqrt{- 4}$

Step 1

Simplify each term.

Rewrite $- 25$ as $- 1 (25)$ .

$\sqrt{- 1 (25)} - \sqrt{- 4}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$\sqrt{- 1} \cdot \sqrt{25} - \sqrt{- 4}$

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

$i \cdot \sqrt{25} - \sqrt{- 4}$

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

$i \cdot \sqrt{5^{2}} - \sqrt{- 4}$

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

$i \cdot 5 - \sqrt{- 4}$

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

$5 \cdot i - \sqrt{- 4}$

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

$5 i - \sqrt{- 1 (4)}$

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

$5 i - (\sqrt{- 1} \cdot \sqrt{4})$

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

$5 i - (i \cdot \sqrt{4})$

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

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

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

$5 i - (i \cdot 2)$

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

$5 i - (2 \cdot i)$

Multiply $2$ by $- 1$ .

$5 i - 2 i$

Step 2

Subtract $2 i$ from $5 i$ .

$3 i$