Can we simplify $\sqrt{a}*\sqrt{a}$ to $a$ when $a \in \mathbb{R}$ and we do not know whether a is positive or negative? (Since $\sqrt{a}$ by itself is undefined in $\mathbb{R}$ when $a$ is negative)
I was wondering about how we can handle the above problem in $\mathbb{R}$ when I had to do some exercise that involved squaring the squareroot in $\mathbb{C}$