Simplify square root of 19/(x^4)

$\sqrt{\frac{19}{x^{4}}}$

Step 1

Rewrite $\frac{19}{x^{4}}$ as ${(\frac{1}{x^{2}})}^{2} \cdot 19$ .

Factor the perfect power $1^{2}$ out of $19$ .

$\sqrt{\frac{1^{2} \cdot 19}{x^{4}}}$

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

$\sqrt{\frac{1^{2} \cdot 19}{{(x^{2})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} \cdot 19}{{(x^{2})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{x^{2}})}^{2} \cdot 19}$

Step 2

Pull terms out from under the radical.

$\frac{1}{x^{2}} \sqrt{19}$

Step 3

Combine $\frac{1}{x^{2}}$ and $\sqrt{19}$ .

$\frac{\sqrt{19}}{x^{2}}$