How does $\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}$ become $1$? [closed]

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

• What have you tried to simplify it? Jun 23 at 10:26

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 $$\sqrt2-1$$.