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%I #26 Jun 27 2023 03:21:23
%S 1,9,1,2,8,2,4,4,0,0,6,0,9,2,8,0,1,6,7,5,1,2,9,5,5,0,6,4,7,8,3,3,5,0,
%T 9,8,9,7,2,3,0,7,2,0,7,2,5,4,5,7,1,9,1,0,5,5,3,7,7,1,1,5,0,8,1,2,5,0,
%U 5,0,9,2,3,3,9,3,9,5,6,1,9,5,8,0,8
%N Decimal expansion of sqrt(28^(1/3)-27^(1/3)).
%C Ramanujan's question 525 (ii), see Berndt and Rankin in References: Show how to find the square roots of surds of the form A^(1/3) + B^(1/3), and hence prove that sqrt(28^(1/3)-27^(1/3)) = (98^(1/3)-28^(1/3)-1)/3.
%C Real root of x^3 + x^2 + 5*x - 1 = 0. - _Hugo Pfoertner_, Sep 12 2018
%D B. C. Berndt and R. A. Rankin, Ramanujan: Essays and Surveys, American Mathematical Society, 2001, ISBN 0-8218-2624-7, page 221 (JIMS 6, page 39 and pages 191-192).
%D Srinivasa Ramanujan, Collected Papers, Chelsea, 1962, page 327, Question 525.
%e 0.191282440060928016751295506478335098972307207254571910553771150812505...
%p evalf(sqrt(28^(1/3)-27^(1/3))); # _Muniru A Asiru_, Aug 28 2018
%t RealDigits[Sqrt[28^(1/3) - 27^(1/3)], 10, 120][[1]] (* _Amiram Eldar_, Jun 27 2023 *)
%o (PARI) sqrt(28^(1/3)-27^(1/3))
%o (PARI) p(x)=x^3+x^2+5*x-1;
%o solve(x=0.18,0.20,p(x)) \\ _Hugo Pfoertner_, Sep 12 2018
%Y Cf. A318521.
%K nonn,cons
%O 0,2
%A _Hugo Pfoertner_, Aug 28 2018
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