α) Είναι:

$$\begin{align} A+Β+Γ & =\big(\sqrt{2}\big)^{6}+\big(\sqrt[3]{3}\big)^{6}+\big(\sqrt[6]{6}\big)^{6}\\ &=\Big(2^{\frac{1}{2}}\Big)^{6}+\Big(3^{\frac{1}{3}}\Big)^{6}+\Big(6^{\frac{1}{6}}\Big)^{6}\\ &= 2^{\frac{6}{2}}+3^{\frac{6}{3}}+6^{\frac{6}{6}}\\ &=8+9+6\\ &=23\end{align}$$

β) Ισχύουν:

$$\sqrt[3]{3}=3^{\frac{1}{3}}=3^{\frac{2}{6}}=\sqrt[6]{3^2}=\sqrt[6]{9}$$

Ακόμα:

$$6\lt 9$$ $$\Leftrightarrow \sqrt[6]{6}\lt \sqrt[6]{9}$$ $$\Leftrightarrow \sqrt[6]{6}\lt \sqrt[3]{3}$$