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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.?

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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.

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  • $\begingroup$ +1 Really thanks for the reference and explanations, what is the mathematical term for the two which is present outside the root and the three which is present inside the root.? I am making a look at the links which was given by you. $\endgroup$ – Rajaprabhu Aravindasamy Jan 12 '14 at 12:33
  • $\begingroup$ The $3$ inside the root is called the "radicand". I'm not aware of any standard name for the $2$ outside the root. $\endgroup$ – Chris Culter Jan 12 '14 at 20:27

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