Defining a real number No answers, please, hints only.
I want to express every nonzero $x\in \mathbb R$ as a product of two numbers that are not rational.
My attempt is $x=(a_1+b_1i)(a_2+b_2i)$ where $a_1, b_2\in \mathbb R$
Am I correct or do I need a hint?

Hints:

*

*Why is addressing the case with positive $x\ne1$ the hard part?

*For such $x$, consider rational and irrational $x$ separately, and think about how $n$th roots would help.

