Simplify square root of 169/(4x^2)

$\sqrt{\frac{169}{4 x^{2}}}$

Rewrite $169$ as $13^{2}$ .

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

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

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

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

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

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

$\frac{13}{2 x}$