What is the #sqrt(3xy)sqrt(27xy^3)#?

1 Answer
Apr 6, 2018

Answer:

The simplified expression is #9xy^2#.

Explanation:

When you have two radicals multiplied together, you can multiply their radicands (the stuff under the radical sign):

#color(white)=sqrt(color(red)3color(blue)xcolor(green)y)*sqrt(color(red)27color(blue)xcolor(green)(y^3))#

#=sqrt(color(red)3color(blue)xcolor(green)y*color(red)27color(blue)xcolor(green)(y^3))#

#=sqrt(color(red)3*color(blue)x*color(green)y*color(red)27*color(blue)x*color(green)(y^3))#

#=sqrt(color(red)3*color(red)27*color(blue)x*color(blue)x*color(green)y*color(green)(y^3))#

#=sqrt(color(red)81*color(blue)(x^2)*color(green)(y^4))#

#=sqrtcolor(red)81*sqrtcolor(blue)(x^2)*sqrtcolor(green)(y^4)#

#=color(red)9*sqrtcolor(blue)(x^2)*sqrtcolor(green)(y^4)#

#=color(red)9*color(blue)x*sqrtcolor(green)(y^4)#

#=color(red)9*color(blue)x*color(green)(y^2)#

#=color(red)9color(blue)xcolor(green)(y^2)#

That's the simplified expression. Hope this helped!