Simplify the Radical Expression 6 square root of 8*2 square root of 3

$6 \sqrt{8} \cdot 2 \sqrt{3}$

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

Factor $4$ out of $8$ .

$6 \sqrt{4 (2)} \cdot 2 \sqrt{3}$

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

$6 \sqrt{2^{2} \cdot 2} \cdot 2 \sqrt{3}$

Pull terms out from under the radical.

$6 (| 2 | \sqrt{2}) \cdot 2 \sqrt{3}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$6 (2 \sqrt{2}) \cdot 2 \sqrt{3}$

Multiply $2$ by $6$ .

$12 \sqrt{2} \cdot 2 \sqrt{3}$

Multiply $2$ by $12$ .

$24 \sqrt{2} \sqrt{3}$

Multiply $24 \sqrt{2} \sqrt{3}$ .

Combine using the product rule for radicals.

$24 \sqrt{3 \cdot 2}$

Multiply $3$ by $2$ .

$24 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$24 \sqrt{6}$

Decimal Form:

$58.78775382 \dots$