Question

given all variables below are positive, express in simplest radical form with a rational denominator.
$\frac{sqrt{48x^{13}y^{10}}}{sqrt{4x^{3}y^{4}}}$

Explanation:

Step1: Combine the radicals

$\frac{\sqrt{48x^{13}y^{10}}}{\sqrt{4x^{3}y^{4}}} = \sqrt{\frac{48x^{13}y^{10}}{4x^{3}y^{4}}}$

Step2: Simplify the fraction inside

$\sqrt{12x^{10}y^{6}}$

Step3: Split the radical into factors

$\sqrt{4 \cdot 3 \cdot (x^5)^2 \cdot (y^3)^2}$

Step4: Simplify perfect square factors

$2x^5y^3\sqrt{3}$

Answer:

$2x^5y^3\sqrt{3}$