I think You can not bring out -3 from radical unless you square it.

your way is correct and because of that when we have (9)1/2----> we have two root -3 and 3 because both make your equation correct.

(3)^2=9

(-3)^2=9

so (9)^(0.5)= 3 or -3

But you are not eligible for bringing out -3 below the radical. so (-3)^0.5 is not possible.you should square -3 below the radical and then bringing it out. this time you are sure the root was -3 not 3 because you have seen it before squaring it.

Best