# Why mathematica cannot get rid of Abs when all variables are positive and reals?

I read a lot of old posts but still couldn't make it work. Hope someone could help me out. I am trying to simplify a square root expression with an assumption that all variables are positive reals. However, why the result sitll has Abssymbol?

vars = {Ao, C1, p, R};
$Assumptions = {vars > 0, Element[vars, Reals]}; FullSimplify[Sqrt[(1 + (1 + Ao)*C1*p*R)^2]]$Assumptions = True;

Output:

Abs[1 + (1 + Ao)*C1*p*R]

Expected output:

1 + (1 + Ao)*C1*p*R
• $Assumptions = Flatten@{Thread[vars > 0], Element[vars, Reals]} – Kuba Commented Mar 22, 2018 at 11:09 • Note that the assumptions mechanism is smart enough to know that if you're using inequality relations, the variables are already assumed real. Thus: Assuming[Thread[{Ao, C1, p, R} > 0], FullSimplify[Sqrt[(1 + (1 + Ao)*C1*p*R)^2]]] Commented Mar 22, 2018 at 11:18 ## 1 Answer Try to rewrite the$Assumptions in the following form

vars = {Ao, C1, p, R};
$Assumptions = And @@ Thread[vars > 0] && Element[vars, Reals]; FullSimplify[Sqrt[(1 + (1 + Ao)*C1*p*R)^2]]$Assumptions = True;

Output (as expected):

1 + (1 + Ao) C1 p R