Question 751341
{{{10 sqrt (1/5) - sqrt (45) - 12 sqrt (5/9)}}}


Let us look at just the square roots having the irrational denominators.


*
{{{sqrt(1/5)=1/sqrt(5)}}}
{{{1/sqrt(5)=(1/sqrt(5))(sqrt(5)/sqrt(5))=highlight(sqrt(5)/5)}}}


*
{{{sqrt(5/9)=sqrt(5/(3*3))=highlight(sqrt(5)/3)}}}



Your expression should now be worked into this:
{{{highlight(10*sqrt(5)/5-sqrt(5*9)-12*sqrt(5)/3)}}}
and that should now be easier to finish simplifying.