I think you just want the simplest radical form of \(\sqrt{192}\)
...if that isn't your question please say so! 
First we want to split 192 into its prime factors.
\(\sqrt{192}=\sqrt{2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3}\)
Then we can rewrite this as:
\(=\sqrt{2\cdot2}\cdot\sqrt{2\cdot2}\cdot\sqrt{2\cdot2}\cdot\sqrt3\)
Replace each \(\sqrt{2\cdot2} \) with 2.
\(=2\cdot2\cdot2\cdot\sqrt3\)
Multiply the numbers outside the radical together.
\(=8\cdot\sqrt3 \\~\\ =8\sqrt3\)
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