First I show what you had, then I show it in a \parbox, trying to use some horizontal list lengths to get the width right (it is close, but not quite right). Finally, I again use a \parbox, but specify the width manually to match the right margin.
To get the proper vertical placement and spacing, I had to use the [t] option of \parbox and also end it with a \strut.
\documentclass{article}
\usepackage{algorithm}
\usepackage{algpseudocode}
\begin{document}
\begin{algorithmic}[1]
\Function {BalanceCascade}{}
\State $i \leftarrow 0, f \leftarrow \sqrt[T-1]{\frac{\left | P \right |}{%
\left | N \right |}}$, some very very very very very very very very very
very very very very very very very long goes here, so this will create a
few new lines
\EndFunction
\Function {BalanceCascade}{}
\State \parbox[t]{\dimexpr\textwidth-\leftmargin-\labelsep-\labelwidth}{%
$i \leftarrow 0, f \leftarrow \sqrt[T-1]{\frac{\left | P \right |}{%
\left | N \right |}}$, some very very very very very very very very very
very very very very very very very long goes here, so this will create a
few new lines\strut}
\EndFunction
\Function {BalanceCascade}{}
\State \parbox[t]{313pt}{%
$i \leftarrow 0, f \leftarrow \sqrt[T-1]{\frac{\left | P \right |}{%
\left | N \right |}}$, some very very very very very very very very very
very very very very very very very long goes here, so this will create a
few new lines\strut}
\EndFunction
\end{algorithmic}
\noindent Here is the left margin
\end{document}

\documentclassand ending with\end{document}. MAybe related Indenting lines of code in algorithm – Bobyandbob May 22 '18 at 17:16\usepackage{varwidth}and try\State \begin{varwidth}[t]{\linewidth} $i \leftarrow 0, f \leftarrow \sqrt[T-1]{\frac{\left | P \right |}{\left | N \right |}}$, some very very very very very very very very very very very very very very very very long goes here, so this will create a few new lines \end{varwidth}... solution from Include a line break in algorithmic while maintaining indentation – Bobyandbob May 22 '18 at 17:25