Simplify square root of 169x^5

$\sqrt{169 x^{5}}$

Step 1

Rewrite $169 x^{5}$ as ${(13 x^{2})}^{2} x$ .

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

$\sqrt{13^{2} x^{5}}$

Factor out $x^{4}$ .

$\sqrt{13^{2} (x^{4} x)}$

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

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

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

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

Step 2

Pull terms out from under the radical.

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