Simplify the following. \(\frac{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}}{\sqrt{16+19.25\times4^2}}\)
Step 1: Innermost: \(\sqrt{225} = 15\); \(\sqrt{154+15} = 13\); \(\sqrt{108+13} = 11\); \(\sqrt{25+11} = 6\); \(\sqrt{10+6} = 4\).
Step 2: Denominator \(= \sqrt{16 + 19.25 \cdot 16} = \sqrt{16 \cdot 20.25} = \sqrt{324} = 18\).
∴ \(\dfrac{4}{18} = \dfrac{2}{9}\)
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