We have 8 = 2 * 4 = 2 * 2^2
so \sqrt{8} = 2 \sqrt{2}
now \sqrt{9} = 3
so \sqrt{\sqrt{9} - \sqrt{8}}
= \sqrt{3 - 2\sqrt{2}}
this is of the form \sqrt{n - 2\sqrt{n-1}} when n = 3
so \sqrt{3 - 2\sqrt{2}} = \sqrt{2 + 1 - 2 * \sqrt{2} * 1}
= \sqrt{(\sqrt{2})^2 + 1^2 - 2 * \sqrt{2} * 1}
= \sqrt{2} - 1
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