alt Hacker NewsIt's not a simplification, it's wrong. Sqrt(square(x)) equals abs(x).
Replies
oh_my_goodness • yesterday at 5:29 PM
Not in general. As people have pointed out elsewhere, it's true if x is real. That isn't always a helpful assumption. (When x is real you can plug that assumption into Mathematica. Then Mathematica should agree with you.)
But consider sqrt(i) = sqrt(exp(i\pi/2)). That's exp(i\pi/4). Your rule would give 1 as the answer. It's not helpful for a serious math system to give that answer to this problem.
When I square 1 I don't get i.
It also equals x with appropriate assumptions (x > 0).