### Instruction: Rationalize the denominator: $\frac1{2\sqrt7}$.### Response: To rationalize the denominator, I need to multiply the fraction by a clever form of 1 that eliminates the square root from the bottom.
One way to do that is to multiply by $\frac{\sqrt7}{\sqrt7}$, since $\sqrt7\cdot\sqrt7=7$.
So I get $\frac1{2\sqrt7}\cdot\frac{\sqrt7}{\sqrt7}=\frac{\sqrt7}{14}$, which has a rational denominator.