How do you simplify #sqrt((x^4y^3)/144)#?

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Answer 1 · 2015-04-09T07:32:48

#color(red)(sqrt((x^4y^3)/144)#

#= sqrt(((x^2)^2*y^2*y)/12^2)#

In general,

#sqrt(a*b) = sqrta * sqrt b#
and
#sqrt(a/b) = sqrt a/ sqrt b#

So the expression will equal

#= (sqrt((x^2)^2)*sqrt(y^2)*sqrty)/(sqrt(12^2))#

#= (x^2*y*sqrty)/(12)#

#= color(green)( ((x^2*y)/12)*sqrt y#