Is this right????
You posted this in the Pre-University Algebra Forum.
That makes it difficult to know what level of mathematics you are doing.
In simple algebra, if $\displaystyle y$ is a real number then $\displaystyle y^2\ge 0$.
Thus $\displaystyle \sqrt{-3}$ does not exist.
But if you are doing advanced algebra and know that there is a complex number $\displaystyle i$ such that $\displaystyle i^2=-1$ then if $\displaystyle y^2=-3$ we have $\displaystyle y=\pm\sqrt3~i$.