Given
indets
restart; expr_with_radical:= 3+x+sqrt(b^2-4*a*c)+sin(y)+x^3*sqrt(39)+sqrt(cos(x));| indets(expr_with_radical, algebraic^fraction)
\( \{ \sqrt {39}, \sqrt {-4 a c +b^{2}}, \sqrt {\cos }x \} \)
Alternative is to use type radical
restart; expr_with_radical:= 3+x+sqrt(b^2-4*a*c)+sin(y)+x^3*sqrt(39)+sqrt(cos(x));| indets(expr_with_radical, radical)
\( \{ \sqrt {39}, \sqrt {-4 a c +b^{2}}, \sqrt {\cos }x \} \)