Evaluate square root of -9+-16

Replace all occurrences of ${\displaystyle +}$${\displaystyle -}$ with a single ${\displaystyle -}$. A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because ${\displaystyle 1\cdot -1=-1}$

Subtract ${\displaystyle 16}$ from ${\displaystyle -9}$.

Rewrite ${\displaystyle -25}$ as ${\displaystyle -1\left(25\right)}$.

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

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

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

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