Why must all possible solutions for radical equations must be checked?

This is not true. Squaring any number gives only one solution. (-4)^2 will always be 16. It will never be anything else.

Radical equations must be checked because squaring both sides can give you two completely different solutions. If you don't check it, you could end up with an incorrect answer. See this website for more information -

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This is not true. Squaring any number gives only one solution. (-4)^2 will always be 16. It will never be anything else.