Simplifying radicals

Question

I am stuck in the following puzzle and couldn't find a way to approach this.

$\sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{14 + \sqrt{180}}}}$

Please help.

Answer 1

$$ \sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{14 + \sqrt{180}}}} = \sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{(\sqrt{5}+3)^2}}} = \sqrt{5 + \sqrt{5} + \sqrt{3 + \sqrt{5} + \sqrt{5} + 3}} = \sqrt{5 + \sqrt{5} + \sqrt{6+2\sqrt{5}}} = \sqrt{5 + \sqrt{5} + \sqrt{(\sqrt{5}+1)^2}} = \sqrt{5 + \sqrt{5} + \sqrt{5}+1}=\sqrt{6+2\sqrt{5}}=\sqrt{5}+1 $$

Answer 2

Hint: $$\eqalign{ & \sqrt{14 + \sqrt {180}} = 3 + \sqrt 5 \cr & \sqrt {3 + \sqrt 5 + 3 + \sqrt 5 } = \sqrt {6 + 2\sqrt 5 } = 1 + \sqrt 5 \cr & \sqrt {5 + \sqrt 5 + \sqrt {3 + \sqrt 5 + 3 + \sqrt 5 } } = \sqrt {6 + 2\sqrt 5 } = 1 + \sqrt 5 \cr} $$