α) Είναι:

\begin{align} A\cdot B\cdot Γ & =\sqrt[3]{5}\cdot \sqrt{3}\cdot \sqrt[6]{5}\\ & =5^{\frac{1}{3}}\cdot \sqrt{3}\cdot 5^{\frac{1}{6}} \\ & =\sqrt{3}\cdot 5^{\frac{1}{3}+\frac{1}{6}} \\ & =\sqrt{3}\cdot 5^{\frac{3}{6}}\\ &=\sqrt{3}\cdot 5^{\frac{1}{2}}\\ &=\sqrt{3}\cdot \sqrt{5}\\ &=\sqrt{15}\end{align}

β) Είναι:

$$ A =\sqrt[3]{5}=5^{\frac{1}{3}}=5^{\frac{2}{6}}=\sqrt[6]{5^{2}}=\sqrt[6]{25}$$

και

$$B=\sqrt{3}=3^{\frac{1}{2}}=3^{\frac{3}{6}}=\sqrt[6]{3^{3}}=\sqrt[6]{27}$$

Ισχύει ότι:

$$25 \lt 27$$ $$\Leftrightarrow \sqrt[6]{25}\lt \sqrt[6]{27}$$ $$\Leftrightarrow A\lt B$$