For a complex number x and integer n, surd(x, n) computes the nth root of x whose (complex) argument is closest to that of x.  Ties are broken in such a way that the function x -> surd(x,n) is  continuous in a counter-clockwise manner onto its branch cuts (that is, continuous in the direction of increasing complex argument).

In particular, if n is odd then if x>=0 then surd(x,n) = x^(1/n) and if x<0 then surd(x,n) = -(-x)^(1/n).

surd(-1, 3);

surd( 8, 3);

surd(-8, 3);

surd(-1, 2);

surd(1+2*I,3);

surd( x, n);

convert((6), power);

Maple simplifies the expression before converting. Constants will still be written with fractional exponents.

convert((9*x)^(1/3), surd);

convert(3^(1/3)*x^(1/2)*a^b+f((-2)^(1/5)*x^(1/n)), surd);

int(surd(x^2,3)*(3*x^3-2*x^2+x-1), x=-2..2);

Note the differences among the outputs of the surd, ^, and root commands.

(8)^(1/3); root(8, 3); surd(8, 3);

(8.0)^(1/3); root(8.0, 3); surd(8.0, 3);

(-8)^(1/3); root(-8, 3); surd(-8, 3);

(-8.0)^(1/3); root(-8.0, 3); surd(-8.0, 3);