Question

simplify. remove all perfect squares from inside the square roots. assume x and y are positive. \\(sqrt{8x^3y^2} = \\) \\(square\\)

Explanation:

Step1: Factor into perfect squares

$\sqrt{8x^3y^2} = \sqrt{4 \cdot 2 \cdot x^2 \cdot x \cdot y^2}$

Step2: Split the square root

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

Step3: Simplify perfect square roots

$2 \cdot x \cdot y \cdot \sqrt{2x}$

Answer:

$2xy\sqrt{2x}$