<s>[INST] which is larger number? $\sqrt{7}-\sqrt{6}$ or $\sqrt{6}-\sqrt{5}$ Which is larger number? $\sqrt{7}-\sqrt{6}$ or $\sqrt{6}-\sqrt{5}$?
Squaring both sides will give me something but I could not go any further.
 [/INST] Let $A = (\sqrt{7}-\sqrt{6}) - (\sqrt{6}-\sqrt{5} )$  
This comes to comes to $A = (\sqrt{7}+\sqrt{5})-2\sqrt{6}$
The square of the first is $12+2\sqrt{35}$, the square of the second is $12+2\sqrt{36}$
Since $35 \lt 36$, then $A \lt 0$, hence $\sqrt{6}-\sqrt{5}$ is bigger.
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