Simplify square root of (8x^3)/(50x)

$\sqrt{\frac{8 x^{3}}{50 x}}$

Reduce the expression $\frac{8 x^{3}}{50 x}$ by cancelling the common factors.

Factor $2$ out of $8 x^{3}$ .

$\sqrt{\frac{2 (4 x^{3})}{50 x}}$

Factor $2$ out of $50 x$ .

$\sqrt{\frac{2 (4 x^{3})}{2 (25 x)}}$

Cancel the common factor.

$\sqrt{\frac{2 (4 x^{3})}{2 (25 x)}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{3}}{25 x}}$

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

Factor $x$ out of $4 x^{3}$ .

$\sqrt{\frac{x (4 x^{2})}{25 x}}$

Cancel the common factors.

Factor $x$ out of $25 x$ .

$\sqrt{\frac{x (4 x^{2})}{x \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{x (4 x^{2})}{x \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{2}}{25}}$

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

$\sqrt{\frac{{(2 x)}^{2}}{25}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{\frac{{(2 x)}^{2}}{5^{2}}}$

Rewrite $\frac{{(2 x)}^{2}}{5^{2}}$ as ${(\frac{2 x}{5})}^{2}$ .

$\sqrt{{(\frac{2 x}{5})}^{2}}$

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

$\frac{2 x}{5}$