A False Answer

Squaring makes two different numbers look alike: -3 and 3 are not equal, but their squares are both 9. So squaring can turn a false equation into a true one, and the squared equation may have answers the original does not.

Take $\sqrt{x+6} = x$. Squaring gives $x+6 = {x}^{2}$, so ${x}^{2}-x-6 = 0$, which factors as $\left(x-3\right)\left(x+2\right) = 0$. The candidates are 3 and -2. Check each in the original. For 3: $\sqrt{9}$ is 3, and the right side is 3. True. For -2: $\sqrt{4}$ is 2, but the right side is -2. False. So -2 is thrown out, and the only answer is 3.

A candidate that the working produces but the original equation rejects is a false answer (textbooks say extraneous). It is not a slip in your algebra: the squaring brought it in. That is why every candidate is checked in the original equation, never in the squared one, where both pass.