sqrt(-3)^2 = sqrt(9) = 3
If you mean
, then you are taking the square root of 9. If, on the other hand, you mean
, then you need to change to complex values:
. . . . .
As soon as you start dealing with negatives inside square roots (or any
even-index root), you have to convert to complex numbers. You gain the ability to deal with negatives inside radicals; you lose the ability to switch around between powers and radicals (so you cannot move the squaring inside and outside and back again).