Question 91071
{{{sqrt(54*x^11)}}}Start with the given expression

{{{sqrt(9*6*x^11)}}} Factor {{{54}}} into {{{9*6}}}
 
{{{sqrt(9*6*x*x^2*x^2*x^2*x^2*x^2)}}} Factor {{{x^11}}} into {{{x*x^2*x^2*x^2*x^2*x^2}}}
 
{{{sqrt(9)*sqrt(6)*sqrt(x)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{3*sqrt(6)*sqrt(x)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)}}} Take the square root of the perfect square {{{9}}} to get 3 
 
{{{3*sqrt(6)*sqrt(x)*x*x*x*x*x}}} Take the square root of the perfect squares {{{x^2}}}  to get x
 
{{{3*sqrt(6)*x^5*sqrt(x)}}} Multiply the common terms 

{{{3*x^5*sqrt(x)*sqrt(6)}}} Rearrange the terms 

{{{3*x^5*sqrt(6x)}}} Group the square root terms