Simplify square root of 6* square root of 12x^3

$\sqrt{6} \cdot \sqrt{12 x^{3}}$

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

Factor $4$ out of $12$ .

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

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

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

Factor out $x^{2}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Combine using the product rule for radicals.

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

Multiply $6$ by $3$ .

$2 x \sqrt{18 x}$

$2 x \sqrt{18 x}$

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

Factor $9$ out of $18$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $2$ .

$6 x \sqrt{2 x}$

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