Remove space between left bracket and square root

Question

Sorry for my bad English.

I have a problem with removing the space between left bracket and multiple root square.

I use code

\documentclass{article}

\usepackage{amsmath}

\usepackage{letltxmacro}

\LetLtxMacro{\oldsqrt}{\sqrt}

\renewcommand{\sqrt}[2][]{\oldsqrt[#1]{#2}}


\begin{document}

$\left(\sqrt{3} \right)$ $\left(\sqrt[3]{4}\right)$ 


\end{document}

But only space in the left one got removed.

Answer 1

Maybe this would suffice. However, it does not (to my mind) work reasonable spacing in other circumstances (post square root), so I would prefer renaming it as \xsqrt or some unique name to be used sparingly.

RE-REVISED to take Heiko's suggestion on how to remove extra space following the square root:

\documentclass{article}
\usepackage{amsmath}
\usepackage{letltxmacro}
\LetLtxMacro{\oldsqrt}{\sqrt}
\renewcommand{\sqrt}[2][\mkern8mu]{\mkern-8mu\mathop{}\oldsqrt[#1]{#2}}
\begin{document}
$\left(\sqrt{3} \right)$ $\left(\sqrt[3]{4}\right)$ 

$x\sqrt{3} x\sqrt[3]{3}$

$y=\sqrt{3} = x = \sqrt[3]{2}$
\end{document}

REVISED:

\documentclass{article}
\usepackage{amsmath}
\usepackage{letltxmacro}
\LetLtxMacro{\oldsqrt}{\sqrt}
\renewcommand{\sqrt}[2][\mkern8mu]{\mkern-4mu\mathop{\oldsqrt[#1]{#2}}}
\begin{document}
$\left(\sqrt{3} \right)$ $\left(\sqrt[3]{4}\right)$ 

$x\sqrt{3} x\sqrt[3]{3}$

$y=\sqrt{3} = x = \sqrt[3]{2}$
\end{document}