Question 148381
{{{sqrt(360)}}}

Find two factors of 360, at least one of which is a perfect square:

36 and 10


So {{{sqrt(360)=sqrt(36)*sqrt(10)}}}


Simplify {{{sqrt(36)}}}


{{{sqrt(360)=6*sqrt(10)}}}




You were well on your way with {{{sqrt(2)*sqrt(180)}}}.  Let's work with it.


Break down 180 into two factors:

36 and 5.


so {{{sqrt(180)=sqrt(36)*sqrt(5)}}}


Again, simplify {{{sqrt(36)}}}

{{{sqrt(180)=6*sqrt(5)}}}


Now plug that into {{{2sqrt(180)}}} and get {{{sqrt(2)*6sqrt(5)}}}


Simplify and get {{{6sqrt(10)}}}


So {{{sqrt(360)=6*sqrt(10)}}}