Simplify square root of 2x^2* square root of 6x

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

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

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

Pull terms out from under the radical.

$x \sqrt{2} \cdot \sqrt{6 x}$

Multiply $x \sqrt{2} \sqrt{6 x}$ .

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Combine using the product rule for radicals.

$x \sqrt{6 x \cdot 2}$

Multiply $2$ by $6$ .

$x \sqrt{12 x}$

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

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Factor $4$ out of $12$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

$2 x \sqrt{3 x}$

Simplify square root of 2x^2* square root of 6x

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