> It can do sqrt(-734/3), but fails on
> sqrt(-244.6666666666667? + 0.?e-39*I)
> for some reason.
>
> Dmitrii

It's worse than failing, it also changes the value:

sage: x = polygen(QQbar)
sage: f = 3*x^4 - 4*x^3 - 1046148*x^2 - 335575956*x - 30288853512
sage: rts = f.roots(multiplicities=False)
sage: r1 = rts[1]
sage: r1
-244.6666666666667? + 0.?e-39*I
sage: r1.sqrt()
...
AttributeError: 'sage.rings.real_mpfi.RealIntervalFieldElement' object
has no attribute 'argument'
sage: r1
-734/3

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