Simplify ( square root of 12x)/(2x^2)

$\frac{\sqrt{12 x}}{2 x^{2}}$

Simplify the numerator.

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

Factor $4$ out of $12$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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