Question 91070
{{{sqrt(72*a^2b^3)}}}Start with the given expression

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

{{{6*ab*sqrt(b)*sqrt(2)}}} Rearrange the terms 

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