Simplify (5 square root of 4)(4 square root of 8)

$(5 \sqrt{4}) (4 \sqrt{8})$

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

$5 \sqrt{2^{2}} (4 \sqrt{8})$

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

$5 \cdot 2 (4 \sqrt{8})$

Multiply $5$ by $2$ .

$10 (4 \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$10 (4 \sqrt{4 (2)})$

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

$10 (4 \sqrt{2^{2} \cdot 2})$

Pull terms out from under the radical.

$10 (4 (2 \sqrt{2}))$

Multiply.

Multiply $2$ by $4$ .

$10 (8 \sqrt{2})$

Multiply $8$ by $10$ .

$80 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$80 \sqrt{2}$

Decimal Form:

$113.13708498 \dots$