Evaluate square root of -16- square root of -25

$\sqrt{- 16} - \sqrt{- 25}$

Step 1

Simplify each term.

Rewrite $- 16$ as $- 1 (16)$ .

$\sqrt{- 1 (16)} - \sqrt{- 25}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$\sqrt{- 1} \cdot \sqrt{16} - \sqrt{- 25}$

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

$i \cdot \sqrt{16} - \sqrt{- 25}$

Rewrite $16$ as $4^{2}$ .

$i \cdot \sqrt{4^{2}} - \sqrt{- 25}$

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

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

Move $4$ to the left of $i$ .

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

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

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

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

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

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

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

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

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

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

$4 i - (i \cdot 5)$

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

$4 i - (5 \cdot i)$

Multiply $5$ by $- 1$ .

$4 i - 5 i$

Step 2

Subtract $5 i$ from $4 i$ .

$- i$