Simplify square root of (13x^2)/(9y^2)

$\sqrt{\frac{13 x^{2}}{9 y^{2}}}$

Rewrite $\frac{13 x^{2}}{9 y^{2}}$ as ${(\frac{x}{3 y})}^{2} \cdot 13$ .

Factor the perfect power $x^{2}$ out of $13 x^{2}$ .

$\sqrt{\frac{x^{2} \cdot 13}{9 y^{2}}}$

Factor the perfect power ${(3 y)}^{2}$ out of $9 y^{2}$ .

$\sqrt{\frac{x^{2} \cdot 13}{{(3 y)}^{2} \cdot 1}}$

Rearrange the fraction $\frac{x^{2} \cdot 13}{{(3 y)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{x}{3 y})}^{2} \cdot 13}$

Pull terms out from under the radical.

$\frac{x}{3 y} \sqrt{13}$

Combine $\frac{x}{3 y}$ and $\sqrt{13}$ .

$\frac{x \sqrt{13}}{3 y}$