Question 116095
{{{sqrt(50*x^2y^20)}}}Start with the given expression

{{{sqrt(25*2*x^2y^20)}}} Factor {{{50}}} into {{{25*2}}}
 
{{{sqrt(25*2*x^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2)}}} Factor {{{x^2y^20}}} into {{{x^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2*y^2}}}
 
{{{sqrt(25)*sqrt(2)*sqrt(x^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)}}} Break up the square root using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{5*sqrt(2)*sqrt(x^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)}}} Take the square root of the perfect square {{{25}}} to get 5 
 
{{{5*sqrt(2)*x*y*y*y*y*y*y*y*y*y*y}}} Take the square root of the perfect squares {{{x^2}}} and {{{y^2}}} to get {{{x}}} and {{{y}}} 
 
{{{5*sqrt(2)*xy^10}}} Multiply the common terms 

{{{5*xy^10*sqrt(2)}}} Rearrange the terms