Can we find a function $f$ such that $f\in C^\infty(\mathbb{R})\cap H^1(\mathbb{R})\cap L^1(\mathbb{R})$ but $(\sqrt{f})' \notin L^2(\mathbb{R})$? [closed]

Can we find a specific function $f$ such that $f\in C^\infty(\mathbb{R})\cap H^1(\mathbb{R})\cap L^1(\mathbb{R})$ but $(\sqrt{f})' \notin L^2(\mathbb{R})$?

Here, $H^1(\mathbb{R})$ denotes the standard Sobolev space containing functions such that $f,f'\in L^2(\mathbb{R})$.