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

Calculate or simplify the expression \( \sqrt{8} \sqrt[3]{3 \frac{y}{6}} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{8}\times \sqrt[3]{3\times \frac{y}{6}}\) - step1: Simplify the root: \(2\sqrt{2}\times \sqrt[3]{3\times \frac{y}{6}}\) - step2: Multiply the terms: \(2\sqrt{2}\times \sqrt[3]{\frac{y}{2}}\) - step3: Use the properties of radicals: \(2\sqrt{2}\times \frac{\sqrt[3]{y}}{\sqrt[3]{2}}\) - step4: Multiply the terms: \(\frac{2\sqrt{2}\times \sqrt[3]{y}}{\sqrt[3]{2}}\) - step5: Multiply the terms: \(\frac{2\sqrt[6]{8y^{2}}}{\sqrt[3]{2}}\) - step6: Simplify: \(2\sqrt[6]{2y^{2}}\) The simplified form of \( \sqrt{8} \sqrt[3]{3 \frac{y}{6}} \) is \( 2\sqrt[6]{2y^{2}} \). This result is a rational number because it can be expressed as a finite decimal or a fraction. Therefore, the result is rational.