#6sqrt2# is the simplest form of what?

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Answer 1 · 2015-10-13T22:34:01

#sqrt(72)#

You're asked to determine what radical term can be simplified to give #6sqrt(2)#.

This means that you have to reverse the process you use when trying to get radical terms to their most simple form.

So, you start with #6sqrt(2)#. Take a look at #6#, is it a perfect square by any chance?

In this case, it is. you know that

#6 = sqrt(6^2) = sqrt(36)#

This means that you can write

#6sqrt(2) = sqrt(36) * sqrt(2)#

You know that

#color(blue)(sqrt(a) * sqrt(b) = sqrt(a * b))#

which means that you have

#6sqrt(2) = sqrt(36) * sqrt(2) = sqrt(36 * 2) = color(green)(sqrt(72))#