Simplify the Radical Expression (3 square root of 2)( square root of 6)

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

Multiply $(3 \sqrt{2}) (\sqrt{6})$ .

Combine using the product rule for radicals.

$3 \sqrt{6 \cdot 2}$

Multiply $6$ by $2$ .

$3 \sqrt{12}$

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

Factor $4$ out of $12$ .

$3 \sqrt{4 (3)}$

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

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

Pull terms out from under the radical.

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

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

$3 (2 \sqrt{3})$

Multiply $2$ by $3$ .

$6 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{3}$

Decimal Form:

$10.39230484 \dots$