Free radicals

Algebra Level 3

5 + 4 + 3 + 2 1 3 1 4 1 5 12 = ? \large \displaystyle{\sqrt[12]{\sqrt[\frac{1}{5}]{5+\sqrt[\frac{1}{4}]{4+\sqrt[\frac{1}{3}]{3+\sqrt{2}}}}}} = \, ?

Give your answer to 3 decimal places.


The answer is 1807.87717.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Hung Woei Neoh
May 10, 2016

Besides using a calculator, I really have no idea how to solve this. Anyone here got a nice solution?

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