Rationalize nested radical expression $\frac{8}{\sqrt{2-\sqrt{\frac{5+\sqrt{5}}{2}}}}$ I have a college task to rationalize this fraction.
$$\frac{8}{\sqrt{2-\sqrt{\frac{5+\sqrt{5}}{2}}}}$$
I do not know how to simplify this fraction. 
Please, explain how to remove the radical from the denominator. Thanks, for your help.

Multiply top and bottom by the denominator to get $$\frac{8}{ \sqrt{2-\sqrt{\frac{5+\sqrt 5}{2}} } }=\frac{8 {\sqrt{2-\sqrt{\frac{5+\sqrt 5}{2}}}} } {2-\sqrt{\frac{5+\sqrt 5}{2}} }.$$ Then multiply top and bottom by $$2+\sqrt{\frac{5+\sqrt 5}{2}},$$ the conjugate of the denominator, to get $$\frac{8 {\sqrt{2-\sqrt{\frac{5+\sqrt 5}{2}}}} \left(2+\sqrt{\frac{5+\sqrt 5}{2}}\right)}{4-\frac{5+\sqrt 5}{2}}.$$ This simplifies to give $$\frac{16 {\sqrt{2-\sqrt{\frac{5+\sqrt 5}{2}}}} \left(2+\sqrt{\frac{5+\sqrt 5}{2}}\right)}{3-\sqrt 5}.$$ Finally multiply by $3+\sqrt 5$ again to get $$\frac{16 {\sqrt{2-\sqrt{\frac{5+\sqrt 5}{2}}}} \left(2+\sqrt{\frac{5+\sqrt 5}{2}}\right)(3+\sqrt 5)}{9-5},$$ which simplifies to give $$4{\sqrt{2-\sqrt{\frac{5+\sqrt 5}{2}}}} \left(2+\sqrt{\frac{5+\sqrt 5}{2}}\right)(3+\sqrt 5).$$
By the way what you did was not rationalise the expression (you can't, since it's not rational). You've only rationalised the denominator.
