A nested radical

The following nested radical was proposed by Srinivasa Ramanujan in [1].

A quick proof of this remarkable identity is the following:

As noted by Ramanujan himself [2], it can be generalized to a vast class of nested radicals, see [3].

References.
[1] S. Ramanujan, J. Indian Math. Soc. 3 (1911), p. 90
[2] S. Ramanujan, J. Indian Math. Soc. 4 (1912), p. 226
[3] K. Srinivasa Rao, G. Vanden Berghe: On an entry of Ramanujan in his Notebooks: a nested roots expansion, Journal of Computational and Applied Mathematics Volume 173, Issue 2, 15 (2005) 371-378, https://doi.org/10.1016/j.cam.2004.04.009

Images Credits: Cliff Pickover (@pickover) and Kai (@UnderAntares) on Twitter