Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $5y^{2}\sqrt{75x^{2}y^{2}}$

Explanation:

Step1: Factor radicand into squares

$\sqrt{75x^2y^2} = \sqrt{25 \cdot 3 \cdot x^2 \cdot y^2}$

Step2: Simplify the radical

$\sqrt{25x^2y^2 \cdot 3} = 5xy\sqrt{3}$

Step3: Multiply with outside term

$5y^2 \cdot 5xy\sqrt{3} = 25xy^3\sqrt{3}$

Answer:

$25xy^3\sqrt{3}$