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

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

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

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

Pull terms out from under the radical.

$x \sqrt{3} \cdot \sqrt{18 x}$

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

Factor $9$ out of $18$ .

$x \sqrt{3} \cdot \sqrt{9 (2) x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

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

Rewrite using the commutative property of multiplication.

$3 x \sqrt{6 x}$