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# i need help

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

May 9, 2017

#1
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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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May 9, 2017