In a standard College Algebra textbook, I encountered the claim that
In many situation, radicands are never formed by raising negative quantities to even powers
Literally the very first exercise problem for the section is then to simplify $\sqrt{(-21)^2}$, which doesn't inspire confidence in the claim. To be clear, I understand that I can't "simplify" this to $-21^{2/2}$ because I know $\sqrt{-21}$ isn't a real number. So why should I start making assumptions when facing expressions like $\sqrt{x^2}$?
How is this claim justified? In what types of situations can I rely on this assumption?
EDIT Perhaps I can be clearer about what I don't understand.
The textbook has given these equalities as tools for simplification when we know that $\sqrt[n]{a}$ exists:
$\sqrt[n]{a^m} = (\sqrt[n]{a})^m = a^{m/n}$
Now, clearly this can't be used to say $\sqrt{-21^2} = -21^{2/2}$, because $\sqrt{-21}$ does not exist (as a real number). So $\sqrt[n]{a^m} = a^{m/n}$ can be useful as a tool for simplification, but it only holds true when making the assumption that radicands aren't being formed by raising negative quantities to even powers.
What I don't understand is why the textbook makes the claim that in most situations radicands are never formed this way.
Since $(-21)^2=21^2$, and since $21\geqslant0$, $\sqrt{(-21)^2}=\sqrt{21^2}=21$. No need for assumptions here.
More generally, if $x\in\Bbb R$, $\sqrt{x^2}=|x|$, since $x^2=|x|^2$ and $|x|\geqslant0$.