Simplify ( square root of 48x^2)/( square root of 3x)

$\frac{\sqrt{48 x^{2}}}{\sqrt{3 x}}$

Step 1

Combine $\sqrt{48 x^{2}}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{48 x^{2}}{3 x}}$

Step 2

Reduce the expression $\frac{48 x^{2}}{3 x}$ by cancelling the common factors.

Factor $3$ out of $48 x^{2}$ .

$\sqrt{\frac{3 (16 x^{2})}{3 x}}$

Factor $3$ out of $3 x$ .

$\sqrt{\frac{3 (16 x^{2})}{3 (x)}}$

Cancel the common factor.

$\sqrt{\frac{3 (16 x^{2})}{3 x}}$

Rewrite the expression.

$\sqrt{\frac{16 x^{2}}{x}}$

Step 3

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

Factor $x$ out of $16 x^{2}$ .

$\sqrt{\frac{x (16 x)}{x}}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$\sqrt{\frac{x (16 x)}{x^{1}}}$

Factor $x$ out of $x^{1}$ .

$\sqrt{\frac{x (16 x)}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (16 x)}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{16 x}{1}}$

Divide $16 x$ by $1$ .

$\sqrt{16 x}$

Step 4

Rewrite $16 x$ as ${(2^{2})}^{2} x$ .

Rewrite $16$ as $4^{2}$ .

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

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Raise $2$ to the power of $2$ .

$4 \sqrt{x}$