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October Surprise 2024

Why can’t you square both sides of an equation?

That’s because the $9$ on the right hand side could have come from squaring a $3$ or from squaring a $-3$. So, when you square both sides of an equation, you can get extraneous answers because you are losing the negative sign. That is, you don’t know which one of the two square roots of the right hand side was there before you squared it.