Question

1. \\(sqrt{32xy^2}\\)

Explanation:

Step1: Factor into perfect squares

$\sqrt{32xy^2} = \sqrt{16 \cdot 2 \cdot x \cdot y^2}$

Step2: Split the square root

$\sqrt{16} \cdot \sqrt{y^2} \cdot \sqrt{2x}$

Step3: Simplify perfect roots

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

Answer:

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