Simplify ( square root of 128x^3)/( square root of 2x)

$\frac{\sqrt{128 x^{3}}}{\sqrt{2 x}}$

Step 1

Combine $\sqrt{128 x^{3}}$ and $\sqrt{2 x}$ into a single radical.

$\sqrt{\frac{128 x^{3}}{2 x}}$

Step 2

Reduce the expression $\frac{128 x^{3}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $128 x^{3}$ .

$\sqrt{\frac{2 (64 x^{3})}{2 x}}$

Factor $2$ out of $2 x$ .

$\sqrt{\frac{2 (64 x^{3})}{2 (x)}}$

Cancel the common factor.

$\sqrt{\frac{2 (64 x^{3})}{2 x}}$

Rewrite the expression.

$\sqrt{\frac{64 x^{3}}{x}}$

Step 3

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

Factor $x$ out of $64 x^{3}$ .

$\sqrt{\frac{x (64 x^{2})}{x}}$

Cancel the common factors.

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

$\sqrt{\frac{x (64 x^{2})}{x^{1}}}$

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

$\sqrt{\frac{x (64 x^{2})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (64 x^{2})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{64 x^{2}}{1}}$

Divide $64 x^{2}$ by $1$ .

$\sqrt{64 x^{2}}$

Step 4

Rewrite $64 x^{2}$ as ${(8 x)}^{2}$ .

$\sqrt{{(8 x)}^{2}}$

Step 5

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

$8 x$