Simplify square root of (81x^2)/(x^4)

$\sqrt{\frac{81 x^{2}}{x^{4}}}$

Step 1

Reduce the expression $\frac{81 x^{2}}{x^{4}}$ by cancelling the common factors.

Factor $x^{2}$ out of $81 x^{2}$ .

$\sqrt{\frac{x^{2} \cdot 81}{x^{4}}}$

Factor $x^{2}$ out of $x^{4}$ .

$\sqrt{\frac{x^{2} \cdot 81}{x^{2} x^{2}}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} \cdot 81}{x^{2} x^{2}}}$

Rewrite the expression.

$\sqrt{\frac{81}{x^{2}}}$

Step 2

Rewrite $81$ as $9^{2}$ .

$\sqrt{\frac{9^{2}}{x^{2}}}$

Step 3

Rewrite $\frac{9^{2}}{x^{2}}$ as ${(\frac{9}{x})}^{2}$ .

$\sqrt{{(\frac{9}{x})}^{2}}$

Step 4

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

$\frac{9}{x}$