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Mahāvīra's Ganita-sara-sangraha I.52 (850 CE) gives the first explicit recognition that √(negative) is undefined on reals. The reasoning: every square is non-negative, so no real number squared yields a negative. Cardano (1545) calls these roots "fictitious"; Bombelli (1572) treats them as imaginary; Gauss (1799) gives the complex-number foundation. The impossibility acknowledgement is Mahāvīra's, ~700 years before Cardano.

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