What could be an element that fulfills the given criteria?

Question

Given that $A=\left \{ x^2|x\in \mathbb{Q}, x^2<2 \right \}$

I want to find an element $y\in A$, with

$|y-2| < 0.001$

There must be a square of a rational number(which thus, is also a rational number) that comes between 1.999 and 2 but i cannot seem to find it.

Answer 1

For instance, $1.4141^2=1.99967881$.