Simplify and clasbify the tesult as rational or irrational \( \sqrt{8} \sqrt[3]{3 \frac{y}{6}} \)

To simplify the expression, we can break it down step by step. First, simplify \( \sqrt{8} \) as \( \sqrt{4 \times 2} = 2\sqrt{2} \). Next, rewrite the cube root: \( \sqrt[3]{3 \frac{y}{6}} \) simplifies to \( \sqrt[3]{\frac{3y}{6}} = \sqrt[3]{\frac{y}{2}} \). Thus, the expression becomes \( 2\sqrt{2} \sqrt[3]{\frac{y}{2}} \). Now, let's classify this result. Since it includes a square root and a cube root mixed together, it generally cannot be expressed as a simple integer or fraction. Therefore, the overall expression is classified as irrational, assuming \( y \) itself is a rational number that doesn’t simplify the roots to rational values.