Simplify ( square root of 12x^6)/( square root of 3x^4)* square root of 4x^2

$\frac{\sqrt{12 x^{6}}}{\sqrt{3 x^{4}}} \cdot \sqrt{4 x^{2}}$

Simplify the numerator.

Rewrite $12 x^{6}$ as ${(2 x^{3})}^{2} \cdot 3$ .

Factor $4$ out of $12$ .

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

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

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

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Move $3$ .

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

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

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

Pull terms out from under the radical.

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

Simplify the denominator.

Rewrite $3 x^{4}$ as ${(x^{2})}^{2} \cdot 3$ .

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

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

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

Pull terms out from under the radical.

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

Simplify terms.

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $2 x^{3} \sqrt{3}$ .

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

Cancel the common factors.

Factor $x^{2}$ out of $x^{2} \sqrt{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $\sqrt{3}$ .

Cancel the common factor.

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

Divide $2 x$ by $1$ .

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

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

$2 x \cdot (2 x)$

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x$

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

Move $x$ .

$2 \cdot 2 (x \cdot x)$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2}$

Multiply $2$ by $2$ .

$4 x^{2}$

Simplify ( square root of 12x^6)/( square root of 3x^4)* square root of 4x^2

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