Use:
There is no rational number whose square equals 2
to show that there is no rational number whose square equals 2/9.
Hello,
Assume there exists a rational number r whose square equals 2/9 :
$\displaystyle r^2=\frac 29$
hence $\displaystyle 9r^2=2$
so $\displaystyle (3r)^2=2$
since r is a rational, 3r is a rational.
But since there is no rational whose square equals 2, we've got a contradiction.