Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form.
$y^{3}\sqrt{25x^{7}y^{3}}$

Explanation:

Step1: Simplify the radical term

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

Step2: Multiply with the external term

$y^3 \cdot 5x^3y\sqrt{xy} = 5x^3 \cdot (y^3 \cdot y) \cdot \sqrt{xy}$

Step3: Combine like variables

$5x^3y^{4}\sqrt{xy}$

Answer:

$5x^3y^4\sqrt{xy}$