Simplify ( square root of -100)( square root of 5)

$(\sqrt{- 100}) (\sqrt{5})$

Step 1

Rewrite $- 100$ as $- 1 (100)$ .

$\sqrt{- 1 (100)} \sqrt{5}$

Step 2

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$\sqrt{- 1} \cdot \sqrt{100} \sqrt{5}$

Step 3

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

$i \cdot \sqrt{100} \sqrt{5}$

Step 4

Rewrite $100$ as $10^{2}$ .

$i \cdot \sqrt{10^{2}} \sqrt{5}$

Step 5

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

$i \cdot 10 \sqrt{5}$

Step 6

Move $10$ to the left of $i$ .

$10 i \sqrt{5}$