If $a = \sqrt{11} - \sqrt{10}$, $b = \sqrt{12} - \sqrt{11}$, and $c = \sqrt{13} - \sqrt{12}$, then which of the following is true?

Rationalising each expression by multiplying and dividing by the conjugate:

$a = \sqrt{11} - \sqrt{10}$

$= \dfrac{(\sqrt{11} - \sqrt{10})(\sqrt{11} + \sqrt{10})}{\sqrt{11} + \sqrt{10}}$

$= \dfrac{11 - 10}{\sqrt{11} + \sqrt{10}}$

$= \dfrac{1}{\sqrt{11} + \sqrt{10}}$

Similarly,

$b = \dfrac{1}{\sqrt{12} + \sqrt{11}}$

$c = \dfrac{1}{\sqrt{13} + \sqrt{12}}$

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Since $\sqrt{10} < \sqrt{11} < \sqrt{12} < \sqrt{13}$, the denominators are in increasing order:

$\sqrt{11} + \sqrt{10} < \sqrt{12} + \sqrt{11} < \sqrt{13} + \sqrt{12}$

All three fractions have the same numerator $= 1$, so a larger denominator gives a smaller value.

$\dfrac{1}{\sqrt{11} + \sqrt{10}} > \dfrac{1}{\sqrt{12} + \sqrt{11}} > \dfrac{1}{\sqrt{13} + \sqrt{12}}$

$a > b > c$