1. Proof

Use:
There is no rational number whose square equals 2
to show that there is no rational number whose square equals 2/9.

2. Hello,
Originally Posted by wvlilgurl
Use:
There is no rational number whose square equals 2
to show that there is no rational number whose square equals 2/9.
Assume there exists a rational number r whose square equals 2/9 :
$r^2=\frac 29$
hence $9r^2=2$

so $(3r)^2=2$

since r is a rational, 3r is a rational.

But since there is no rational whose square equals 2, we've got a contradiction.