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RealDigits[Sqrt[Surd[1/5, 5]+Surd[4/5, 5]], 10, 120][[1]] (* Harvey P. Dale, Dec 14 2021 *)

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S. Ramanujan, Coll. Papers, Chelsea, 1962, page 334, Question 1070.

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allocatedDecimal forexpansion Hugoof Pfoertnersqrt((1/5)^(1/5)+(4/5)^(1/5)).

1, 2, 9, 6, 5, 8, 4, 8, 0, 7, 6, 6, 5, 0, 1, 8, 3, 0, 7, 4, 9, 2, 4, 0, 1, 6, 4, 5, 8, 2, 9, 1, 3, 5, 7, 7, 7, 4, 8, 5, 1, 3, 5, 2, 1, 3, 4, 8, 5, 3, 0, 2, 2, 6, 1, 4, 2, 7, 4, 3, 1, 4, 1, 8, 0, 8, 9, 6, 1, 9, 4, 0, 5, 0, 6, 2, 0, 3, 2, 7, 7, 8, 6, 3, 6, 1

1,2

Ramanujan's question 1070 (i) asks for a proof of the identities

sqrt((1/5)^(1/5)+(4/5)^(1/5)) = (1+2^(1/5)+8^(1/5))^(1/5) = (16/125)^(1/5)+(8/125)^(1/5)+(2/125)^(1/5)-(1/125)^(1/5).

1.296584807665018307492401645829135777485135213485302261427431418...

(PARI) sqrt((1/5)^(1/5)+(4/5)^(1/5))

Cf. A318524, A318525.

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Hugo Pfoertner, Aug 28 2018

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