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

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

Step 1

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

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

Step 2

Reduce the expression $\frac{12 x}{3 x}$ by cancelling the common factors.

Factor $3$ out of $12 x$ .

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

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{\frac{4 x}{x}}$

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

$\sqrt{\frac{4 x}{x}}$

Divide $4$ by $1$ .

$\sqrt{4}$

Step 4

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

$\sqrt{2^{2}}$

Step 5

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

$2$