TITLE: Whats the rule for putting up a plus-minus sign when taking under root?
QUESTION [10 upvotes]: Given a simple equation....   
$\ (x+1)^2 =21 $     
if we take the under root of both sides , we get 
$\ x+1 = \pm \sqrt{21} $  
why dont we get a $ \pm $ on the left hand side ?

REPLY [2 votes]: More interesting is to check out what happens with an inequality:
$$ y^2 \le 4 $$
Since the y-values that satisfy the inequality are between -2 to 2, we write:
$$ |y| \le 2 $$
Without using any step showing plus/minus. In any equation or inequation all we're doing is trying to show which values satisfy it. Thinking of mathematics as a set 'rules' to follow isn't the best way to go about doing it.