Question 184502
{{{2*sqrt(27*x^5y)}}} Start with the given expression



{{{2*sqrt(9*3*x^5y)}}} Factor 27 into {{{9*3}}}. Note: one of the factors is a perfect square.


{{{2*sqrt(9*3*x^2*x^2*x*y)}}} Factor {{{x^5}}} into {{{x^2*x^2*x}}}.



{{{2*sqrt(9)*sqrt(3)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y)}}} Break up the square root.



{{{2*3*sqrt(3)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y)}}} Take the square root of 9 to get 3



{{{2*3*sqrt(3)*x*x*sqrt(x)*sqrt(y)}}} Take the square root of {{{x^2}}} to get "x". Note: {{{x>=0}}}



{{{6x^2*sqrt(3xy)}}} Multiply and rearrange the terms.



So {{{2*sqrt(27*x^5y)=6x^2*sqrt(3xy)}}} where every variable is nonnegative