TITLE: Which is more simplified: $a\sqrt{b}$ or $\sqrt{c}$?
QUESTION [6 upvotes]: Which is considered more simplified (if it matters)?
$a \sqrt{b}$ or $\sqrt{c}$
For example:
$2 \sqrt{3}$ or $\sqrt{12}$

REPLY [2 votes]: As a general rule, simpler means having fewer symbols. So $\sqrt6$ is simpler than $\sqrt2\sqrt3$. In your case, the number of symbols is the same; so another rule kicks in: small numbers are simpler than big ones. So $2\sqrt3$ is simpler than $\sqrt{12}$. However, it's debatable whether $2^7$ is simpler than $128$, because decimal notation is considered more basic and familiar than taking powers. Ultimately, the question of which is simpler may come down to a matter of taste.