Frank Day

2022-07-11

How show the $\sqrt{2}×\sqrt{2}=2=\frac{2}{1}$ symbolically?

Melina Richard

Expert

$\sqrt{2}\in \mathbb{R}\mathrm{\setminus }\mathbb{Q}$ but $\left(\sqrt{2}{\right)}^{2}=2\in \mathbb{Q}$, $\mathbb{R}\mathrm{\setminus }\mathbb{Q}$ is not closed under multiplication.