Which is larger, $\sqrt{10} - \sqrt{9}$ or $\sqrt{11} - \sqrt{10}$?

Explanation

1. 01

   $\sqrt{n + 1} - \sqrt{n} = \frac{1}{\sqrt{n + 1} + \sqrt{n}}$, on multiplying top and bottom by $\sqrt{n + 1} + \sqrt{n}$.

2. 02

   The denominator $\sqrt{10} + \sqrt{9}$ is smaller than $\sqrt{11} + \sqrt{10}$, so $\sqrt{10} - \sqrt{9}$ is larger.