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?

Hint. Play with examples.

*

*$2=\sqrt{2}\cdot \sqrt{2}$

*$-4=\frac{-4}{\sqrt{3}}\cdot \sqrt{3}$.

*$\frac{7}{5}=\sqrt{\frac{7}{5}}\cdot\sqrt{\frac{7}{5}}$

*$\sqrt{2}=\frac{\sqrt{2}}{2}\cdot 2\sqrt{2}$

*etc.

Now generalize...
