Question

given all variables below are positive, express in simplest radical form with a rational denominator.
$\frac{sqrt{144x^{6}}}{sqrt{9x^{2}}}$

Explanation:

Step1: Combine square roots

$\frac{\sqrt{144x^6}}{\sqrt{9x^2}} = \sqrt{\frac{144x^6}{9x^2}}$

Step2: Simplify fraction inside root

$\sqrt{\frac{144}{9} \cdot \frac{x^6}{x^2}} = \sqrt{16x^4}$

Step3: Evaluate square root

$\sqrt{16x^4} = 4x^2$

Answer:

$4x^2$