What is \sqrt{17-4\sqrt{15}}+\sqrt{8-2\sqrt{15}} equal to ?

Explanation

Express each term as a perfect square: \sqrt{17-2\sqrt{60}} = \sqrt{(\sqrt{12}-\sqrt{5})^2} = 2\sqrt{3}-\sqrt{5}. Similarly, \sqrt{8-2\sqrt{15}} = \sqrt{(\sqrt{5}-\sqrt{3})^2} = \sqrt{5}-\sqrt{3}. Adding them: (2\sqrt{3}-\sqrt{5}) + (\sqrt{5}-\sqrt{3}) = \sqrt{3}.

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