Find the Product (3 square root of 6)(2 square root of 3)

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

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

Multiply $2$ by $3$ .

$6 \sqrt{6} \sqrt{3}$

Combine using the product rule for radicals.

$6 \sqrt{3 \cdot 6}$

Multiply $3$ by $6$ .

$6 \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$6 \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical.

$6 (3 \sqrt{2})$

Multiply $3$ by $6$ .

$18 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt{2}$

Decimal Form:

$25.45584412 \dots$