Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form.
$y^{2}\sqrt{25x^{7}y^{7}}$

Explanation:

Step1: Simplify the radical term

$\sqrt{25x^7y^7} = \sqrt{25} \cdot \sqrt{x^7} \cdot \sqrt{y^7} = 5 \cdot x^3\sqrt{x} \cdot y^3\sqrt{y}$

Step2: Rewrite combined radical

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

Step3: Multiply by outer term $y^2$

$y^2 \cdot 5x^3y^3\sqrt{x y} = 5x^3y^{2+3}\sqrt{x y}$

Step4: Simplify exponent of $y$

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

Answer:

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