def real_root(arg, n=None):
    """Return the real nth-root of arg if possible. If n is omitted then
    all instances of (-n)**(1/odd) will be changed to -n**(1/odd); this
    will only create a real root of a principle root -- the presence of
    other factors may cause the result to not be real.

    Examples
    ========

    >>> from sympy import root, real_root, Rational
    >>> from sympy.abc import x, n

    >>> real_root(-8, 3)
    -2
    >>> root(-8, 3)
    2*(-1)**(1/3)
    >>> real_root(_)
    -2

    If one creates a non-principle root and applies real_root, the
    result will not be real (so use with caution):

    >>> root(-8, 3, 2)
    -2*(-1)**(2/3)
    >>> real_root(_)
    -2*(-1)**(2/3)


    See Also
    ========

    sympy.polys.rootoftools.rootof
    sympy.core.power.integer_nthroot
    root, sqrt
    """
    from sympy import im, Piecewise
    if n is not None:
        try:
            n = as_int(n)
            arg = sympify(arg)
            if arg.is_positive or arg.is_negative:
                rv = root(arg, n)
            else:
                raise ValueError
        except __HOLE__:
            return root(arg, n)*Piecewise(
                (S.One, ~Equality(im(arg), 0)),
                (Pow(S.NegativeOne, S.One/n)**(2*floor(n/2)), And(
                    Equality(n % 2, 1),
                    arg < 0)),
                (S.One, True))
    else:
        rv = sympify(arg)
    n1pow = Transform(lambda x: -(-x.base)**x.exp,
                      lambda x:
                      x.is_Pow and
                      x.base.is_negative and
                      x.exp.is_Rational and
                      x.exp.p == 1 and x.exp.q % 2)
    return rv.xreplace(n1pow)

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dataset/ETHPy150Open sympy/sympy/sympy/functions/elementary/miscellaneous.py/real_root