Why is it necessary to check for extraneous solutions in radical equations?

Extraneous solutions mean "extra and not necessary"

Example: the area of a square = 16, what is the side of the square:

:If a is the side, the area is a²:

a² = 16, the square root of a = + √16 or a = - √16:

a = 4 or a = - 4, Obviously you can't have a side of - 4, then this solution is an extraneous one