Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $6\sqrt{25x^{2}y^{3}}$

Explanation:

Step1: Factor radicand into perfect squares

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

Step2: Simplify each perfect square factor

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

Step3: Multiply by the leading coefficient

$6 \cdot 5xy\sqrt{y}$

Answer:

$30xy\sqrt{y}$