Simplify (8 square root of 100)(7 square root of -49)

$(8 \sqrt{100}) (7 \sqrt{- 49})$

Rewrite $- 49$ as $- 1 (49)$ .

$8 \sqrt{100} (7 \sqrt{- 1 (49)})$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$8 \sqrt{100} (7 (\sqrt{- 1} \cdot \sqrt{49}))$

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

$8 \sqrt{100} (7 (i \cdot \sqrt{49}))$

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

$8 \sqrt{10^{2}} (7 (i \cdot \sqrt{49}))$

Multiply.

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

$8 \cdot 10 (7 (i \cdot \sqrt{49}))$

Multiply $8$ by $10$ .

$80 (7 (i \cdot \sqrt{49}))$

Rewrite $49$ as $7^{2}$ .

$80 (7 (i \cdot \sqrt{7^{2}}))$

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

$80 (7 (i \cdot 7))$

Move $7$ to the left of $i$ .

$80 (7 (7 \cdot i))$

Multiply $7$ by $7$ .

$80 (49 i)$

Multiply $49$ by $80$ .

$3920 i$