$$\frac{{\sqrt {10 + \sqrt {25 + \sqrt {108 + \sqrt {154 + \sqrt {225} } } } } }}{{\root 3 \of 8 }} = ?$$

Explanation:-

$$\eqalign{ & \frac{{\sqrt {10 + \sqrt {25 + \sqrt {108 + \sqrt {154 + \sqrt {225} } } } } }}{{\root 3 \of 8 }} \cr & \Rightarrow \frac{{\sqrt {10 + \sqrt {25 + \sqrt {108 + \sqrt {169} } } } }}{2} \cr & \Rightarrow \frac{{\sqrt {10 + \sqrt {25 + \sqrt {121} } } }}{2} \cr & \Rightarrow \frac{{\sqrt {10 + \sqrt {36} } }}{2} \cr & \Rightarrow \frac{{\sqrt {16} }}{2} \cr & \Rightarrow \frac{4}{2} \cr & \Rightarrow 2 \cr}$$