Simplify ( square root of 96x^3)/( square root of 2x)

$\frac{\sqrt{96 x^{3}}}{\sqrt{2 x}}$

Step 1

Combine $\sqrt{96 x^{3}}$ and $\sqrt{2 x}$ into a single radical.

$\sqrt{\frac{96 x^{3}}{2 x}}$

Step 2

Reduce the expression $\frac{96 x^{3}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $96 x^{3}$ .

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

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

$\sqrt{\frac{x (48 x^{2})}{x}}$

Cancel the common factors.

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

$\sqrt{\frac{x (48 x^{2})}{x^{1}}}$

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

$\sqrt{\frac{x (48 x^{2})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (48 x^{2})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{48 x^{2}}{1}}$

Divide $48 x^{2}$ by $1$ .

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

Step 4

Rewrite $48 x^{2}$ as ${(4 x)}^{2} \cdot 3$ .

Factor $16$ out of $48$ .

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

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

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

Move $3$ .

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

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

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

Step 5

Pull terms out from under the radical.

$4 x \sqrt{3}$