# When to use exponent rule sqrt(x^2) and when to square both sides?

When to use exponent rule ${\sqrt{x}}^{2}$ and when to square both sides?
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juicilysv
If $y=f\left(x\right)$ is a function then if you ever have an $\left({x}_{1},{y}_{1}\right)$ you can not have an $\left({x}_{1},{y}_{2}\right)$ unless ${y}_{1}={y}_{2}$
so that should tell you that if you ever have $x=\sqrt{1-{y}^{2}}$ then as ${y}^{2}=\left(-y{\right)}^{2}$ you will also have $x=\sqrt{1-\left(-y{\right)}^{2}}$ so if you ever have $\left(x,y\right)$ you will also have $\left(x,-y\right)$ and if $y\ne 0$ then $y\ne -y$ so it can't be a function.