Simplify 5 square root of 9- square root of -64

$5 \sqrt{9} - \sqrt{- 64}$

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

$5 \sqrt{3^{2}} - \sqrt{- 64}$

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

$5 \cdot 3 - \sqrt{- 64}$

Multiply $5$ by $3$ .

$15 - \sqrt{- 64}$

Rewrite $- 64$ as $- 1 (64)$ .

$15 - \sqrt{- 1 (64)}$

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$15 - (\sqrt{- 1} \cdot \sqrt{64})$

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

$15 - (i \cdot \sqrt{64})$

Rewrite $64$ as $8^{2}$ .

$15 - (i \cdot \sqrt{8^{2}})$

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

$15 - (i \cdot 8)$

Move $8$ to the left of $i$ .

$15 - (8 \cdot i)$

Multiply $8$ by $- 1$ .

$15 - 8 i$