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$$\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}$$ The answer to this question is "1" but I have no idea how !! Please show the steps to solve the problem.

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    $\begingroup$ What have you tried to simplify it? $\endgroup$
    – ConMan
    Jun 23 at 10:26

1 Answer 1

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Square $$\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}$$ to observe that $$\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}=\sqrt2.$$ Now denest $\sqrt{3-2\sqrt2}$ to $\sqrt2-1$.

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