Square root of 512k^2. show work

square root of 512k^2
Problem:Simplify
 512k2 −−−−−√ Step-By-Step Solution:Rewrite 512k2 as (16k)2⋅2.More Steps(16k)2⋅2−−−−−−−−√Pull terms out from under the radical.16k2√

(I don't seem to have a raical on this thing, so this _/ will have to serve as one) you take the _/512 and the _/k^2 the squared root of k^2 is simply k. the squared root of 512, however, is not so simple. you are going to have to factor it out. so 512 factors into a bunch of numbers. we want to root it. it would be approximately 22.84732. so 22 will not be a factor. now. let's divide 512 by two. 216. now divide that by two. 108. so. we've by two how many times? we are going to want to multiply all of this up until we find a few like terms. I have found a few threes in the mix. so I have 2*2*2*2*3*3*3. so as you can see have two 12s and a three left over. so we have the under the radical _/12^2*3. twelve squared can now get out of the radial and become 12_/3. so your answer will be 12_/3 * k.