Question 83596
{{{ 3b(sqrt(27a^5b)) + 2a(sqrt(3a^3b^3))}}} Start with the given expression


{{{ 3b(sqrt(9*3*a^2*a^2*a*b)) + 2a(sqrt(3*a^2*a*b^2*b))}}} Factor 27 into 9*3, {{{a^5}}} into {{{a^2*a^2*a}}}, {{{a^3}}} into {{{a^2*a}}}, and {{{b^3}}} into {{{b^2*b}}}


{{{ 3b(sqrt(9)*sqrt(3)*sqrt(a^2)*sqrt(a^2)*sqrt(a*b)) + 2a(sqrt(3)*sqrt(a^2)*sqrt(a)*sqrt(b^2)*sqrt(b))}}} Break up the square roots



{{{ 3b(3*sqrt(3)*a*a*sqrt(a*b)) + 2a(sqrt(3)*a*sqrt(a)*b*sqrt(b))}}} Take the square root of all the perfect squares



{{{ 3b(3a^2*sqrt(3)*sqrt(a*b)) + 2a(ab*sqrt(3)*sqrt(a)*sqrt(b))}}} Multiply



{{{ 3b(3a^2*sqrt(3ab)) + 2a(ab*sqrt(3ab))}}} Combine any left over square roots


{{{ 9a^2b*sqrt(3ab) + 2a^2b*sqrt(3ab))}}} Multiply


{{{ (9a^2b+2a^2b)*sqrt(3ab)) }}} Combine like terms


{{{ 11a^2b*sqrt(3ab) }}} Add. So this is the simplified expression