Demonstrating a principle by example:
#sqrt(an)=sqrt(a)xxsqrt(n)#
#sqrt(4xx25)=2xx5=10#
#sqrt(4xx25)=sqrt(100)=10#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:#" "sqrt(15n^2)xxsqrt(10n^3)#
#" "[sqrt(3)xxsqrt(5)xxcolor(blue)(sqrt(n^2))]xx[sqrt(2)xxsqrt(5)xxcolor(red)(sqrt(n^2))xxsqrt(n)]#
#larr" "color(blue)(n)[sqrt(3)xxsqrt(5)]" "xx" "color(red)(n)[sqrt(2) xxsqrt(5)xxsqrt(n)]#
#|" "#......................................................................................................
#|#
#|#
#rarr" "color(brown)(n)[sqrt(3)xxcolor(blue)(sqrt(5))]" "xx" "color(brown)(n)[sqrt(2) xxcolor(blue)(sqrt(5))xxsqrt(n)]#
#" "color(blue)(5)color(brown)(n^2)[sqrt(3)xxsqrt(2)xxsqrt(n)] #
#color(white)()#
#" "5n^2sqrt(6n)#