1) If $\displaystyle x$ is a positive real number, then $\displaystyle x^2$ is a positive real number. Therefore, if $\displaystyle a^2$ is positive, where $\displaystyle a$ is a real number, then $\displaystyle a$ is a positive real number.

2) If $\displaystyle x^2 /= 0$, where $\displaystyle x$ is a real number, then $\displaystyle x /= 0$. Let a be areal number with $\displaystyle a^2 /= 0$; then $\displaystyle a /= 0$