PGFplot of sqrt x error

Question

I'm trying to plot the square and cubic root of x using this code:

\begin{tikzpicture}[scale=.5, >=stealth]
             
    \begin{axis}[
        xmin=-5,xmax=5,
        ymin=-5,ymax=5,
        axis x line=middle,
        axis y line=middle,
        axis line style=<->,
        ]
        \addplot[no marks,blue] expression[samples=100]{sqrt{x}} 
                    node[pos=0.65,anchor=south west]{$y=\sqrt{x}$}; 
                    
        \addplot[no marks,red] expression[domain=-pi:pi,samples=100]{sqrt[3]{x}} 
                    node[pos=0.65,anchor=south west]{$y=\sqrt[3]{x}$}; 
    \end{axis}
\end{tikzpicture}

but I get the following errors:

I've tried writing \sqrt instead of sqrt but the errors are the same. How can I solve this?

---

Ok so, trying, as suggested by a comment, to try different formulas I got it working with x^(1/2) and x^(1/3)

The problem now is that I get the wrong graph for the cube root.

The code now is:

             \begin{tikzpicture}[scale=.5, >=stealth]
             
    \begin{axis}[
        xmin=-5,xmax=5,
        ymin=-5,ymax=5,
        axis x line=middle,
        axis y line=middle,
        axis line style=<->,
        ]
        \addplot[no marks,blue] expression[domain=0:5,samples=100]{x^(1/2)} 
                    node[pos=0.65,anchor=south west]{$y=\sqrt{x}$}; 
                    
        \addplot[no marks,red] expression[domain=-5:5,samples=100]{x^(1/3)} 
                    node[pos=0.65,anchor=south west]{$y=\sqrt[3]{x}$}; 
    \end{axis}
\end{tikzpicture}

But for the cube root I'm missing the negative branch:

How can I solve this?

Answer 1

I don't really know why TikZ can't plot correctly but here is a trick: graph of x^(1/3) is same as (x^3,x) (if I am not mistaken):

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{tikz,pgfplots}
\begin{document}
    \begin{tikzpicture}[scale=1, >=stealth]
    
    \begin{axis}[
    xmin=-5,xmax=5,
    ymin=-5,ymax=5,
    axis x line=middle,
    axis y line=middle,
    axis line style=<->,
    ]
    \addplot[red,domain=-5:5,samples=100]({x^(3)},{x})
    node[pos=0.65,anchor=south]{$y=\sqrt[3]{x}$};
    \end{axis}
    \end{tikzpicture}
\end{document}