<s>[INST] Simplifying expression $\sqrt{6+2\sqrt{5}} - \sqrt{6-2\sqrt{5}}.$ I'm stuck. Squaring it will change it's value. Is there any general method of simplifying expressions of the form $$\sqrt{a+b}-\sqrt{a-b} = c \ \ ?$$
 [/INST] It's clearly positive. Its square is
$$a^2=6+2\sqrt 5+6-2\sqrt 5-2\sqrt{(6+2\sqrt5)(6-2\sqrt5)}
=12-2\sqrt{16}=4$$
so $a=2$.
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