[Tex/LaTex] differences when using inline mode and \overline and \sqrt

Question

Can anyone help me make this square root signs in the code below, be of the same size so that they all have the same height? This is the code:

\documentclass[]{book}


\begin{document}

$\overline{\sqrt{v_{x}^{2}}}$ and 
$\overline{\sqrt{v_{y}^{2}}}$ and 
$\overline{\sqrt{v_{h}^{2}}}$


\end{document}

Thanks

EDIT (13/08/2018):

\documentclass[a4paper]{book}

\usepackage[]{biblatex}

\usepackage{graphicx}
\usepackage{subfig} %for subfigures


\begin{document}

\begin{figure}%
\centering
\subfloat[SUB CAPTION TEXT]{{\includegraphics[width=.48\textwidth]{image1.pdf} }}%
~
\subfloat[SUB CAPTION TEXT]{{\includegraphics[width=.48\textwidth]{image2.pdf} }}%
\newline
\subfloat[SUB CAPTION TEXT]{{\includegraphics[width=.48\textwidth]{image3.pdf} }}%
~
\subfloat[SUB CAPTION TEXT]{{\includegraphics[width=.48\textwidth]{image4.pdf} }}%
\caption{$\overline{\sqrt{v_{\vphantom{h}\smash{y}}^{2}}}$}%
\label{fig:du}%
\end{figure} 

\end{document}

Answer 1

Here are solutions, based on \smash and \vphantom:

\documentclass[]{book}

\begin{document}

$\overline{\sqrt{v_{x}^{2}}}$ and
$\overline{\sqrt{v_{\smash{y}}^{2}}}$ and
$\overline{\sqrt{v_{h}^{2}}}$\\

If you’re a perfectionist, you can also have the exponent 2 at the same height: \\

$\overline{\sqrt{v_{\vphantom{h}x}^{2}}}$ and
$\overline{\sqrt{v_{\vphantom{h}\smash{y}}^{2}}}$ and
$\overline{\sqrt{v_{h}^{2}}}$

\end{document}