Defining range of variables for the whole notebook

Questions
1

Hi all,
At the start of a notebook, is there a way to define that a parameter belongs to a specific range such as [0,1]? I need Mathematica to know about the sign of the values under radicals and simplify them without being forced to repeat the Assuming function for the whole notebook over and over.

2

You could use $Assumptions

$Assumptions = {a > 0, b > 0};

Sqrt[a^2*b^2] // Simplify
(* a b *)

Power[a^3*b^3, 1/3] // Simplify
(* a b *)