Simplify (6 square root of 5)(- square root of -100)

$(6 \sqrt{5}) (- \sqrt{- 100})$

Step 1

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

$6 \sqrt{5} (- \sqrt{- 1 (100)})$

Step 2

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

$6 \sqrt{5} (- (\sqrt{- 1} \cdot \sqrt{100}))$

Step 3

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

$6 \sqrt{5} (- (i \cdot \sqrt{100}))$

Step 4

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

$6 \sqrt{5} (- (i \cdot \sqrt{10^{2}}))$

Step 5

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

$6 \sqrt{5} (- (i \cdot 10))$

Step 6

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

$6 \sqrt{5} (- (10 \cdot i))$

Step 7

Multiply $10$ by $- 1$ .

$6 \sqrt{5} (- 10 i)$

Step 8

Multiply $- 10$ by $6$ .

$- 60 \sqrt{5} i$