Question 96818
{{{sqrt(72*x^3)}}}Start with the given expression

{{{sqrt(36*2*x^3)}}} Factor {{{72}}} into {{{36*2}}}
 
{{{sqrt(36*2*x*x^2)}}} Factor {{{x^3}}} into {{{x*x^2}}}
 
{{{sqrt(36)*sqrt(2)*sqrt(x)*sqrt(x^2)}}} Break up the square root using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{6*sqrt(2)*sqrt(x)*sqrt(x^2)}}} Take the square root of the perfect square {{{36}}} to get 6 
 
{{{6*sqrt(2)*sqrt(x)*x}}} Take the square root of the perfect squares {{{x^2}}} to get {{{x}}} 
 
{{{6*sqrt(2)*x*sqrt(x)}}} Multiply the common terms 

{{{6*x*sqrt(x)*sqrt(2)}}} Rearrange the terms 

{{{6*x*sqrt(2x)}}} Group the square root terms