Simplify square root of (25x)/(x^3)

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

Step 1

Reduce the expression $\frac{25 x}{x^{3}}$ by cancelling the common factors.

Factor $x$ out of $25 x$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

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

$\frac{5}{x}$