How to know if there is a extraneous solution in a radical expression I was trying to solve this problem:
$$\sqrt{3x+13} = x+ 3$$
So I was pretty confident about this problem and started solving:
$$(\sqrt{3x+13})^2 = (x+ 3)^2$$
$$(3x+13) = (x+ 3)^2$$
$$3x+13 = x^2 + 6x + 9$$
$$0 = x^2 + 3x - 4$$
$$0 = (x+4)(x-1)$$
So my final answer was $x = -4$ and $ x = 1 $. However, it was incorrect because when I plug back in -4 into the original equation I get a extraneous solution. My question is do I always need to plug back in my answers into a radical expression and check if they are valid? Or is there any other way to deduce that there will be a extraneous solution?

On its domain ($A\ge 0$), note that
$$\sqrt A=B\iff A=B^2\enspace\textbf{and}\enspace B\ge 0,$$
since the symbol$\sqrt{\phantom{h}}$ denotes the non-negative square root of a non-negative real number.
