# Need a mathematical name for a particular conversion.

I can convert 12 into 2 $\def\sf{\sqrt 3}\sf$

But I don't know the correct mathematical name for this conversion. can anyone tell me the exact mathematical name for this process and link me to the details of the same.?

The operation that turns the number $12$ into $2\sqrt3$ is the square root. One writes $\sqrt{12}=2\sqrt3$.
I gather that you're asking how we get the formal expression $2\sqrt3$ from $\sqrt{12}$. In elementary algebra textbooks, $2\sqrt3$ is called the "simplest radical form" or the "simplified form" of the radical $\sqrt{12}$. There's a little more detail at Wikipedia.
• The $3$ inside the root is called the "radicand". I'm not aware of any standard name for the $2$ outside the root. – Chris Culter Jan 12 '14 at 20:27