Question 171500
Share a problem and someone will try to help you.  In general, if you are factoring the expression under a radical, look for factors that are perfect squares.


For example, if you are faced with {{{sqrt(c)}}}, but you know that {{{c=a^2b}}}, then you can write {{{sqrt(c)=sqrt(a^2b)=a*sqrt(b)}}}


For a specific example, simplify {{{sqrt(12)}}}.  We know that {{{12=4*3}}}, but since {{{4=2^2}}}, {{{12 = 2^2*3}}}, so {{{sqrt(12)=sqrt(2^2*3)=2*sqrt(3)}}}


For a more complex specific example, consider {{{sqrt(r^2*s+2rs+s)}}}


Factor {{{r^2*s+2rs+s}}} completely:  {{{s(r+1)(r+1)=s(r+1)^2}}}.  Now we have:


{{{sqrt(r^2*s+2rs+s)=sqrt(s(r+1)^2)}}} which can be written {{{(r+1)sqrt(s)}}}