Question

question
given all variables below are positive, express in simplest radical form with a rational denominator.
\\(\frac{\sqrt{180x^{10}y^{6}}}{\sqrt{9x^{2}y^{3}}}\\)

Explanation:

Step1: Combine radicals into one

$\frac{\sqrt{180x^{10}y^6}}{\sqrt{9x^2y^3}} = \sqrt{\frac{180x^{10}y^6}{9x^2y^3}}$

Step2: Simplify the fraction inside

$\sqrt{20x^{8}y^3}$

Step3: Factor into perfect squares

$\sqrt{4x^8y^2 \cdot 5y}$

Step4: Extract perfect square roots

$\sqrt{4x^8y^2} \cdot \sqrt{5y} = 2x^4y\sqrt{5y}$

Answer:

$2x^4y\sqrt{5y}$