\documentclass{article}

\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[official]{eurosym}

\def\eurocodepoint{20AC}
\DeclareUnicodeCharacter{\eurocodepoint}{\textbf\euro}
\DeclareUnicodeCharacter{221A}{\sqrt}

\begin{document}
  The amount is 10€ and 2 cents.

  A square root $√{x^2+1}$.
\end{document}
