Question

using the quotient property of radicals
what is \\(\frac{\sqrt{25x^2y^3}}{\sqrt{xy}}\\) in simplest form? assume \\(x \geq 0\\) and \\(y \geq 0\\).
\\(5\sqrt{xy}\\) \\(\sqrt{5xy}\\) \\(5xy\sqrt{xy}\\) \\(25\sqrt{xy}\\)

Explanation:

Step1: Apply quotient property of radicals

$\frac{\sqrt{25x^2y^2}}{\sqrt{xy}} = \sqrt{\frac{25x^2y^2}{xy}}$

Step2: Simplify the fraction inside

$\sqrt{25x^{2-1}y^{2-1}} = \sqrt{25xy}$

Step3: Simplify the radical

$\sqrt{25xy} = \sqrt{25} \cdot \sqrt{xy} = 5\sqrt{xy}$

Answer:

$5\sqrt{xy}$