Simplify square root of (13x^2)/(4y^2)

$\sqrt{\frac{13 x^{2}}{4 y^{2}}}$

Step 1

Rewrite $\frac{13 x^{2}}{4 y^{2}}$ as ${(\frac{x}{2 y})}^{2} \cdot 13$ .

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

$\sqrt{\frac{x^{2} \cdot 13}{4 y^{2}}}$

Factor the perfect power ${(2 y)}^{2}$ out of $4 y^{2}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Combine $\frac{x}{2 y}$ and $\sqrt{13}$ .

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