Simplify square root of 18x^2*4 square root of 3x^2

$\sqrt{18 x^{2}} \cdot 4 \sqrt{3 x^{2}}$

Rewrite using the commutative property of multiplication.

$4 \sqrt{18 x^{2}} \sqrt{3 x^{2}}$

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

Factor $9$ out of $18$ .

$4 \sqrt{9 (2) x^{2}} \sqrt{3 x^{2}}$

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

$4 \sqrt{3^{2} \cdot 2 x^{2}} \sqrt{3 x^{2}}$

Move $2$ .

$4 \sqrt{3^{2} x^{2} \cdot 2} \sqrt{3 x^{2}}$

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$4 \sqrt{{(3 x)}^{2} \cdot 2} \sqrt{3 x^{2}}$

Pull terms out from under the radical.

$4 (3 x \sqrt{2}) \sqrt{3 x^{2}}$

Simplify the expression.

Multiply $3$ by $4$ .

$12 (x \sqrt{2}) \sqrt{3 x^{2}}$

Reorder $3$ and $x^{2}$ .

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

Pull terms out from under the radical.

$12 x \sqrt{2} (x \sqrt{3})$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$12 (x \cdot x) \sqrt{2} \sqrt{3}$

Multiply $x$ by $x$ .

$12 x^{2} \sqrt{2} \sqrt{3}$

Multiply $12 x^{2} \sqrt{2} \sqrt{3}$ .

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$12 x^{2} \sqrt{6}$