Question

assuming x and y are both positive, write the following expression in simplest radical form.
$y^{3}\sqrt{8x^{4}y^{2}}$

Explanation:

Step1: Factor radicand into perfect squares

$\sqrt{8x^4y^2} = \sqrt{4 \cdot 2 \cdot (x^2)^2 \cdot y^2}$

Step2: Simplify the radical

$\sqrt{4 \cdot 2 \cdot (x^2)^2 \cdot y^2} = 2x^2y\sqrt{2}$

Step3: Multiply with external term

$y^3 \cdot 2x^2y\sqrt{2} = 2x^2y^{3+1}\sqrt{2}$

Step4: Combine like variables

$2x^2y^{4}\sqrt{2}$

Answer:

$2x^2y^4\sqrt{2}$