Simplify (4 square root of 3)/( square root of 12)

$\frac{4 \sqrt{3}}{\sqrt{12}}$

Combine $\sqrt{3}$ and $\sqrt{12}$ into a single radical.

$4 \sqrt{\frac{3}{12}}$

Cancel the common factor of $3$ and $12$ .

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Factor $3$ out of $3$ .

$4 \sqrt{\frac{3 (1)}{12}}$

Cancel the common factors.

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Factor $3$ out of $12$ .

$4 \sqrt{\frac{3 \cdot 1}{3 \cdot 4}}$

Cancel the common factor.

$4 \sqrt{\frac{3 \cdot 1}{3 \cdot 4}}$

Rewrite the expression.

$4 \sqrt{\frac{1}{4}}$

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$4 \frac{\sqrt{1}}{\sqrt{4}}$

Any root of $1$ is $1$ .

$4 \frac{1}{\sqrt{4}}$

Simplify the denominator.

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

$4 \frac{1}{\sqrt{2^{2}}}$

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

$4 (\frac{1}{2})$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$2 (2) \frac{1}{2}$

Cancel the common factor.

$2 \cdot 2 \frac{1}{2}$

Rewrite the expression.

$2$

Simplify (4 square root of 3)/( square root of 12)

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