Question 171504
You started on the right track.


Prime factorization of 128

128/2 = 64
64/2 = 32
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1


So there are 7 factors of 2 that make 128.  Put another way, {{{128=2^7}}}


Also, {{{2^7}}} can be expressed as {{{2*2^6}}}


Therefore {{{sqrt(128)=sqrt(2*2^6)=2^3*sqrt(2)=8*sqrt(2)}}}


Let's see if this answer makes sense:


{{{8*sqrt(2)*8*sqrt(2)=64*2=128}}}.  Yep, that works.