Simplify $\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}$ Simplify $\displaystyle{\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}}$.
I get this when I was doing another Q,
but I don't know how to further simplify it.
Can anyone help me, please?

Hint: Let's note $o:=\frac {1+\sqrt{5}}2$, $a:=\sqrt{10-2\sqrt{5}}$ and $b:=\sqrt{5+2\sqrt{5}}$
then $ab=\sqrt{30+10\sqrt{5}}=5+\sqrt{5}$
Compute $(o\cdot a+b)^2$ to conclude.
