+0

# i need help

0
221
1

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

Guest May 9, 2017
#1
+7164
+2

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

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.

$$=8\cdot\sqrt3 \\~\\ =8\sqrt3$$

hectictar  May 9, 2017