Simplify square root of 6x^2* square root of 48x

$\sqrt{6 x^{2}} \cdot \sqrt{48 x}$

Reorder $6$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 6} \cdot \sqrt{48 x}$

Pull terms out from under the radical.

$x \sqrt{6} \cdot \sqrt{48 x}$

Rewrite $48 x$ as ${(2^{2})}^{2} \cdot (3 x)$ .

Factor $16$ out of $48$ .

$x \sqrt{6} \cdot \sqrt{16 (3) x}$

Rewrite $16$ as $4^{2}$ .

$x \sqrt{6} \cdot \sqrt{4^{2} \cdot 3 x}$

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

$x \sqrt{6} \cdot \sqrt{{(2^{2})}^{2} \cdot 3 x}$

Add parentheses.

$x \sqrt{6} \cdot \sqrt{{(2^{2})}^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$x \sqrt{6} \cdot (2^{2} \sqrt{3 x})$

Raise $2$ to the power of $2$ .

$x \sqrt{6} \cdot (4 \sqrt{3 x})$

Multiply $x \sqrt{6} (4 \sqrt{3 x})$ .

Combine using the product rule for radicals.

$x (4 \sqrt{6 (3 x)})$

Multiply $6$ by $3$ .

$x (4 \sqrt{18 x})$

Rewrite using the commutative property of multiplication.

$4 x \sqrt{18 x}$

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

Factor $9$ out of $18$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $3$ by $4$ .

$12 x \sqrt{2 x}$