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What is 192−−−√192 expressed in simplest radical form?

 May 9, 2017
 #1
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+2

I think you just want the simplest radical form of \(\sqrt{192}\)

...if that isn't your question please say so! smiley

 

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.

\(=8\cdot\sqrt3 \\~\\ =8\sqrt3\)

.
 May 9, 2017

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