Question 807023
Well:

We can actually tell right off the bat this is irrational, because of the{{{sqrt(27)}}} component.

The {{{sqrt(27)}}} does not have a rational number as a perfect square. The {{{sqrt(27)}}} is 5.1961524227066318805823390245176171008284157614311418. 

Now if we add the two to this number we get:

7.1961524227066318805823390245176171008284157614311418

Now we need to determine this is an irrational number.

Rational numbers of counting numbers, natural numbers, integers, whole numbers, fractions, and repeating decimals ie.(2.2323...)

Since this number does not match any of these definitions, we can determine that {{{2+sqrt(27)}}} is not rational.

Hope this Helps!