Gauge Terrell

2022-07-02

Let $a$ and $b$ be irrational numbers. when do we have $a\cdot b$ = rational number?
for example $\sqrt{2}\cdot \sqrt{2}=2$.

Alexzander Bowman

Expert

Exactly when one is a rational multiple of the other's reciprocal.
Ex: $\sqrt{2}×\frac{3}{\sqrt{2}}$ is rational, but $\sqrt{2}×\frac{\pi }{\sqrt{2}}$ is irrational.

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