Common differentiable approximation of $f(x) = |x|$ and $f(x,y) = \sqrt{x^2+y^2}$

Question

Is there a common approximation (like commonly used in applications) of the functions

$$ f(x) = |x| $$

and it's two variable version

$$ f(x,y) = \sqrt{x^2 + y^2} $$

I'm trying to come up with a potential function of similar expression, but I have the issue that these two aren't differentiable in $0$.