Aus Online Mathematik Brückenkurs 1

The expression \displaystyle -3^2 means \displaystyle -(3^2)= -9 (and not \displaystyle (-3)^2) and so we have that

\displaystyle \sqrt{-3^2} = \sqrt{-9}\,\textrm{.}

The root expression \displaystyle \sqrt{-9} is not defined because there is no number which, when multiplied by itself, gives \displaystyle -9.