#math/algebra The equations $y^{2}=x$ and $y=\sqrt{x}$ are related but not the same. The former implies $ y^{2}=x \iff y=\pm \sqrt{x}. $ Since $y^{2}=9$ has solutions $y=9$ and $y=-9$. When we say directly $y=\sqrt{x}$, it is only the positive or non-negative branch of $y^{2}=x$.