How do you find the simplest radical form of 12?

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Answer 1 · 2018-03-25T02:37:12

The simplified radical form of #sqrt12# is #2sqrt3#.

We need to utilize these two radical rules:

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

#color(red)sqrt(color(black)a^2)=a#

To solve our problem, first, factor #12# into its prime factorization, then apply those two rules. Here's what that will look like:

#color(white)=sqrt12#

#=sqrt(color(red)4*color(blue)3)#

#=sqrt(color(red)(2*2)*color(blue)3)#

#=sqrt(color(red)(2^2)*color(blue)3)#

#=sqrtcolor(red)(2^2)*sqrtcolor(blue)3#

#=color(red)2*sqrtcolor(blue)3#

#=color(red)2sqrtcolor(blue)3#

That's as simplified as it gets. Hope this helped!