Find the Product (5 square root of 2+4)(5 square root of 2-4)

$(5 \sqrt{2 + 4}) (5 \sqrt{2 - 4})$

Simplify by adding and subtracting.

Add $2$ and $4$ .

$5 \sqrt{6} (5 \sqrt{2 - 4})$

Subtract $4$ from $2$ .

$5 \sqrt{6} (5 \sqrt{- 2})$

Rewrite $- 2$ as $- 1 (2)$ .

$5 \sqrt{6} (5 \sqrt{- 1 (2)})$

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$5 \sqrt{6} (5 (\sqrt{- 1} \cdot \sqrt{2}))$

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

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

Multiply $5 \sqrt{6} (5 i \sqrt{2})$ .

Multiply $5$ by $5$ .

$25 \sqrt{6} (i \sqrt{2})$

Combine using the product rule for radicals.

$25 \sqrt{2 \cdot 6} i$

Multiply $2$ by $6$ .

$25 \sqrt{12} i$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$25 \sqrt{4 (3)} i$

Rewrite $4$ as $2^{2}$ .

$25 \sqrt{2^{2} \cdot 3} i$

Pull terms out from under the radical.

$25 (2 \sqrt{3}) i$

Multiply $2$ by $25$ .

$50 \sqrt{3} i$