Question: How can one create a spiral of roots as shown in the diagram below:

![enter image description here](https://i.stack.imgur.com/HfRHi.png)

where one can use a command to draw more parts to the spiral. For example, a command like `\sqrtspiral{1}`, `\sqrtspiral{2}`, `\sqrtspiral{3}` would generate the image above. 

NOTE
----

I am inviting all solutions in TikZ, PSTricks, Asymptote and possibly MetaPost. So many ways to achieve the same diagram.

Answer: 
While I've not labeled the sides, here's something:

```
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\pagestyle{empty}
\def\mylast{6}
\begin{document}

\begin{tikzpicture}
  \coordinate (ORIGIN) at (0,0) ;
  \coordinate (LAST)   at (1,0) ;
  \draw (ORIGIN) -- (LAST) ;
  \foreach \myitem in {2,3,...,\mylast}
  {
    \coordinate (NEXT) at ($(LAST)!1cm!-90:(ORIGIN)$) ;
    \draw (LAST) -- (ORIGIN) -- (NEXT) -- cycle;
    \coordinate (LAST) at (NEXT);
  }
\end{tikzpicture}

\end{document}

```

![enter image description here](https://i.stack.imgur.com/NSoD4.png)

**UPDATE**

Here's an initial attempt at adding some labels. Not the best, but again, I'll look more into this later.

```
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\pagestyle{empty}
\def\mylast{12}
\begin{document}

\begin{tikzpicture}
  \coordinate (ORIGIN) at (0,0) ;
  \coordinate (LAST)   at (2,0) ;
  \foreach \myitem in {1,2,3,...,\mylast}
  {
    \coordinate (NEXT) at ($(LAST)!2cm!-90:(ORIGIN)$) ;
    \draw (LAST) -- (ORIGIN) -- (NEXT) -- cycle;
    \node (MID) at ($(LAST)!0.5!(ORIGIN)$)   {};
    \expandafter\def\csname mylbl\mylast\endcsname{$\sqrt{\myitem}$}
    \node (LBL\myitem) at ($(MID)!0.75em!90:(LAST)$) {\footnotesize\csname mylbl\mylast\endcsname};
    \node at ($($(LAST)!0.5!(NEXT)$)!0.5em!90:(LAST)$) {1};
    %% right angle
    \coordinate (perpA) at ($(LAST)!0.5em!(NEXT)$);
    \coordinate (perpB) at ($(perpA)!0.5em!-90:(LAST)$);
    \coordinate (perpC) at ($(LAST)!0.5em!(ORIGIN)$);
    \draw (perpA) -- (perpB) -- (perpC);
    %% reset "LAST" for next iteration
    \coordinate (LAST) at (NEXT);
  }
\end{tikzpicture}

\end{document}

```

![enter image description here](https://i.stack.imgur.com/EXNOp.png)
I guess that this can help you. Since I want to post the image I am posting as an answer (even partial). 

See [23.2 pg. 144](http://mirrors.ctan.org/macros/latex/contrib/tkz/tkz-euclide/doc/tkz-euclide-screen.pdf) from the guide of [tkz-euclide](http://www.ctan.org/tex-archive/macros/latex/contrib/tkz/tkz-euclide).

![enter image description here](https://i.stack.imgur.com/fxODc.png)