Question 739933
{{{2-sqrt(5)}}} is irrational because {{{sqrt(5)}}} is irrational.
You know that the result from adding, or subtracting, or multiplying rational numbers is always rational.
If {{{a}}} is rational, {{{2-a}}} must be rational.
If {{{2-sqrt(5)}}} was rational,
{{{2-(2-sqrt(5))=2-2+sqrt(5)=sqrt(5)}}} would be rational,
but it is not.
 
NOTE:
Watch out for trick questions.
Sometimes rational numbers are written in an unusual way to make them look irrational, just to trick you.
{{{sqrt(4)=2}}} is a rational number, even when it is written as {{{sqrt(4)}}}
Similarly, {{{sqrt(9/4)=3/2}}} is rational, and so is
{{{sqrt(12)/sqrt(3)=sqrt(4*3)/sqrt(3)=sqrt(4)*sqrt(3)/sqrt(3)=2*sqrt(3)/sqrt(3)=2}}}